Assumptions

201 questions

Question 41Question →

Archaeologist: Recent excavations of the ancient settlement of Tlanex indicate a stark division in material culture. The highland sector contains thousands of intricately carved jade artifacts, whereas the lowland sector contains almost exclusively unpolished clay implements. Because the jade artifacts required hundreds of hours of specialized labor to produce, they were undoubtedly luxury items of immense value. Consequently, the inhabitants of the highland sector must have belonged to a significantly higher socioeconomic class than the inhabitants of the lowland sector.

Which one of the following is an assumption required by the archaeologist's argument?

Show answer & explanation

Answer: The artifacts recovered from the highland and lowland sectors were not deposited by a single population that utilized the two sectors for different societal functions.

Answer

The argument requires assuming that the artifacts recovered from the highland and lowland sectors were not deposited by a single population that utilized the two sectors for different societal functions.
To test if an assumption is necessary, we apply the Negation Technique: we make the statement false and see if the argument survives. If we negate the correct answer, it becomes: 'The artifacts recovered from the highland and lowland sectors WERE deposited by a single population that utilized the two sectors for different societal functions.' If the exact same group of people simply used the highland sector for one thing (e.g., storing wealth or ceremonies) and the lowland sector for another (e.g., farming or daily work), then there are no distinct 'inhabitants of the highland sector' to compare against 'inhabitants of the lowland sector.' Because negating this statement completely destroys the argument, the original statement is a logically necessary assumption.

Step-by-Step Solution

1
Identify the conclusion of the argument.
The inhabitants of the highland sector belonged to a significantly higher socioeconomic class than the inhabitants of the lowland sector.
This sets the target for the necessary assumption. The author is making a comparative claim about two distinct groups of people.
2
Identify the premises supporting the conclusion.
The highland sector contains immensely valuable luxury jade artifacts, while the lowland sector contains almost exclusively unpolished clay implements.
This establishes the evidence used to draw the conclusion: a geographical division of material wealth.
3
Find the logical gap between the premises and the conclusion.
The author equates 'where artifacts are found' with 'where distinct socioeconomic classes lived'.
The author assumes the artifacts represent two different populations living in two different areas, rather than one population using different areas for different tasks (e.g., living in the highlands and working in the lowlands).
4
Apply the Negation Technique to the correct option to verify it is necessary.
Negated correct option: 'The artifacts WERE deposited by a single population that utilized the two sectors for different societal functions.'
If this negated statement is true, there are no separate 'highland inhabitants' and 'lowland inhabitants' to compare. The entire argument collapses, proving this assumption is strictly necessary.

Key Concept

Defender Assumption / Negation Technique
Question 42Question →

Agricultural Scientist: The new Lumina strain of tomatoes has been genetically modified to produce a natural compound that repels the silverleaf whitefly, a major agricultural pest. In controlled greenhouse trials, Lumina plants suffered 80 percent less whitefly damage than conventional tomato plants. Therefore, transitioning to the Lumina strain in our region's commercial outdoor farms will undoubtedly lead to a significant increase in overall tomato yields.

Which one of the following is an assumption required by the agricultural scientist's argument?

Show answer & explanation

Answer: The natural compound produced by the Lumina strain does not repel the insects that are necessary for pollinating tomatoes in outdoor farms.

Answer

The correct answer is the option stating that the natural compound produced by the Lumina strain does not repel the insects necessary for pollinating tomatoes.
This is a required assumption because applying the logical negation technique destroys the argument's conclusion. If we negate this statement to read, 'The natural compound produced by the Lumina strain DOES repel the insects that are necessary for pollinating tomatoes in outdoor farms,' the argument falls apart. If the plants repel the very insects needed to pollinate them, they will not bear fruit, making a 'significant increase in overall tomato yields' impossible. Thus, the scientist must assume the natural pesticide does not have this catastrophic side effect.

Step-by-Step Solution

1
Identify the conclusion of the argument.
Transitioning to the Lumina strain in commercial outdoor farms will lead to a significant increase in overall tomato yields.
Understanding the exact scope of the conclusion ('significant increase in overall yields' in 'outdoor farms') is critical for finding the necessary gap.
2
Identify the premises supporting the conclusion.
Lumina plants produce a compound that repels whiteflies, and in greenhouse trials, they suffered 80 percent less damage from this pest.
This establishes the evidence used to predict the future success of the crop.
3
Spot the logical gap in the reasoning.
The argument shifts from controlled greenhouse success (reducing pest damage) to outdoor agricultural success (increasing actual fruit yield).
Yield requires more than just pest resistance; in an outdoor environment, other factors (like pollination) are crucial.
4
Apply the Negation Technique to the answer choices.
Negating the correct option results in: 'The compound DOES repel the insects necessary for pollinating.' This directly destroys the possibility of increasing tomato yields.
A necessary assumption is one that, if proven false, completely dismantles the argument.

Key Concept

Applying the Negation Technique to identify necessary assumptions that rule out fatal alternative explanations (Defender Assumptions).
Question 43Question →

Sociologist: A recent corporate study found that employees who participated in an optional weekly mindfulness meditation program reported a 40 percent lower rate of workplace stress compared to employees who did not participate. This demonstrates that practicing mindfulness meditation directly reduces workplace stress.

Which one of the following is an assumption required by the sociologist's argument?

Show answer & explanation

Answer: The employees who participated in the mindfulness meditation program did not have significantly lighter workloads than the employees who did not participate.

Answer

The assumption that participating employees did not have significantly lighter workloads than non-participating employees.
This option is a necessary defender assumption because it eliminates a critical alternate explanation. The study compared two groups: those who opted into the program and those who did not. If the participants had significantly lighter workloads, that lighter workload—rather than the meditation—could easily explain their lower stress levels. By stating this was not the case, the assumption defends the author's causal claim. When negated (the participants DID have lighter workloads), the argument collapses.

Step-by-Step Solution

1
Identify the conclusion and the premise of the argument.
Conclusion: Mindfulness meditation directly reduces workplace stress. Premise: Employees who participated in an optional meditation program reported 40% lower stress than non-participants.
Deconstructing the argument is the first step to evaluating its logical gaps.
2
Analyze the reasoning structure and identify the flaw.
The argument moves from a correlation (participation and lower stress) to a causal claim. The flaw is failing to consider alternate explanations for why the participants had lower stress.
Causal conclusions drawn from observational studies are vulnerable to third-variable confounders and selection bias.
3
Determine what a necessary assumption must do in this context.
A necessary assumption must defend the causal claim by ruling out a plausible alternate explanation (a 'Defender' assumption).
To prove the argument depends on a statement, negating that statement must destroy the argument.
4
Apply the negation technique to the correct option.
Negating the correct option yields: 'The employees who participated DID have significantly lighter workloads.' This provides an alternate cause for the lower stress, destroying the original conclusion.
The negation test definitively proves whether an assumption is logically necessary.

Key Concept

Ruling Out Alternate Explanations in Causal Arguments
Question 44Question →

A recent study of adult diets revealed that individuals who drink at least one cup of green tea daily have a significantly lower incidence of heart disease compared to those who do not drink green tea. The researchers concluded that consuming green tea actively protects against the development of heart disease.

Which of the following are necessary assumptions upon which the researchers' causal argument depends? (Select all that apply)

Select all that apply

Show answer & explanation

Answer: The individuals in the study who drank green tea did not also engage in other heart-healthy behaviors at significantly higher rates than the non-drinkers.; People who naturally have healthier cardiovascular systems do not inherently crave green tea more than those with poorer cardiovascular health.

Answer

The correct answers are the statements ruling out alternate causes for the lower heart disease incidence (such as other healthy behaviors) and ruling out reverse causation (the possibility that having a naturally healthy heart causes one to crave green tea).
The argument assumes that the observed correlation is truly a direct causal relationship. For this to be logically sound, the researchers must assume that other factors (like additional healthy lifestyle choices) did not independently cause the lower heart disease rate, and they must also assume that having a naturally healthy heart did not simply cause a preference for green tea. The correct statements perfectly address and rule out these two specific causal threats (alternate cause and reverse causation).

Step-by-Step Solution

1
Identify the argument's premises and main conclusion.
Premise: There is a correlation between drinking green tea and a lower incidence of heart disease. Conclusion: Drinking green tea actively protects against heart disease.
Understanding the structure of the argument is required before analyzing its logical gaps.
2
Identify the core logical flaw or gap.
The argument jumps from a mere correlation in a study to an absolute causal relationship.
In logical reasoning, observing that two things happen together does not automatically prove that one caused the other.
3
Determine the necessary assumptions required to bridge this causal gap.
A valid causal conclusion requires assuming that there are no alternate causes for the effect, that the relationship is not backward (reverse causation), and that the correlation is not purely coincidental.
These are the standard assumptions any causal argument must rely upon to be logically sound.
4
Evaluate the given options using the negation test.
Negating the statement about alternate healthy behaviors or the statement about reverse craving destroys the argument's causal claim, confirming they are both necessary assumptions.
If an assumption is truly necessary, its logical negation will severely weaken or destroy the main conclusion.

Key Concept

Assumptions in Causal Arguments
Question 45Question →

An archaeologist argues: 'Pottery fragments from the ancient Zanthian culture found in coastal excavations are consistently much harder than those found at inland Zanthian sites. This proves that centuries of exposure to salty coastal air chemically strengthened the clay.'

To protect this causal argument from criticism, the archaeologist must assume several 'defender' statements that rule out alternate explanations. Match each alternate explanatory objection below to the specific defender assumption that logically neutralizes it.

Click a left item, then click its matching right item

Items

The coastal Zanthians may have fired their pottery at much higher temperatures than inland Zanthians did.
The raw clay deposits available in the coastal region might have naturally contained more hardening silicates than inland deposits.
The harsh coastal climate may have completely destroyed all but the most durable pottery, whereas inland conditions preserved weaker pieces.
Coastal Zanthians might have deliberately designed their pottery to be substantially thicker to withstand rough ocean travel.

Matches

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Answer

The correct matches pair each specific alternate causal explanation with the negative assumption that explicitly rules it out. The firing temperature objection matches the assumption about kiln heat; the raw clay objection matches the assumption about unworked geological materials; the climate destruction objection matches the assumption about environmental filtering; and the deliberate thickness objection matches the assumption about structural dimensions.
Each correct pair successfully matches a specific threat to the argument's causal conclusion with the negative assumption that neutralizes that precise threat. In Logical Reasoning, when an author argues that A causes B based on an observed difference, they necessarily assume that no other factor (C, D, or E) caused that difference. Mapping the specific alternate explanation to its corresponding negative assumption demonstrates mastery of how 'defender' assumptions operate.

Step-by-Step Solution

1
Analyze the core argument.
The archaeologist concludes that salty air (cause) strengthened the coastal pottery (effect), based solely on the correlation that coastal pottery is harder than inland pottery.
Understanding the exact cause and effect relationship is necessary to identify vulnerabilities in the reasoning.
2
Identify the role of a defender assumption in a causal argument.
A defender assumption must protect the causal conclusion by eliminating a plausible alternate explanation (confounding variable) for the observed difference in pottery hardness.
This establishes the criteria for a correct match: the assumption must directly negate the specific alternate cause.
3
Evaluate the first objection (firing temperatures) and locate the matching assumption.
The objection regarding higher firing temperatures is neutralized by the assumption that there was no significant difference in the heat levels of the kilns used.
Ruling out a difference in manufacturing heat explicitly defends against the manufacturing alternate explanation.
4
Evaluate the second objection (raw clay composition) and locate the matching assumption.
The objection regarding natural hardening silicates is neutralized by the assumption that unworked geological materials were not inherently stronger on the coast.
Ruling out baseline material differences defends against the raw resources alternate explanation.
5
Evaluate the third objection (coastal climate destruction) and locate the matching assumption.
The objection regarding the destruction of weaker pottery is neutralized by the assumption that environmental erosion did not act as a disproportionate filter.
Ruling out survivorship bias defends against the sample selection alternate explanation.
6
Evaluate the fourth objection (thicker designs) and locate the matching assumption.
The objection regarding thicker design for ocean travel is neutralized by the assumption that the structural dimensions and thickness were essentially comparable.
Ruling out differences in physical design defends against the structural alternate explanation.

Key Concept

Defender Assumptions in Causal Reasoning (Ruling Out Alternate Explanations)
Question 46Question →

Match each logical argument to the specific statement that, if assumed, enables the argument's conclusion to be properly drawn.

Click a left item, then click its matching right item

Items

Any philosophical framework that fundamentally relies on purely theoretical entities violates the established principle of parsimony, rendering it methodologically suspect. Consequently, string theory inherently violates this foundational principle of parsimony. This is because its core mathematical models necessarily posit the existence of multiple extra spatial dimensions beyond the observable universe.
The newly proposed municipal planning reform will undoubtedly alleviate the city's severe and persistent housing shortage. The legislation completely abolishes a series of outdated and restrictive zoning ordinances. Empirical economic evidence demonstrates conclusively that removing such archaic restrictions invariably stimulates the local construction sector to build high-density developments.
A central bank's monetary policy can successfully curb runaway inflation only if it significantly diminishes aggregate consumer spending within the economy. Therefore, the central bank's recent aggressive series of interest rate hikes will successfully curb inflation, as preliminary market data indicates these rate hikes have already begun to diminish consumer spending.
The corporate board's unilateral decision to rapidly liquidate the struggling subsidiary's assets was clearly and objectively unethical. In executing this liquidation, the board explicitly prioritized the immediate distribution of shareholder dividends over the long-term financial security and well-being of the subsidiary's dedicated workforce.

Matches

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Answer

Argument 1 pairs with the definition of theoretical entities; Argument 2 pairs with the construction sector guarantee; Argument 3 pairs with the economic intervention sufficiency; Argument 4 pairs with the moral principle on corporate ethics.
Each correct pairing provides the exact missing premise required to make its corresponding argument formally valid. This involves bridging concept gaps, connecting intermediate steps to final outcomes, fixing conditional logic flaws, and supplying underlying moral principles.

Step-by-Step Solution

1
Analyze the philosophical argument regarding string theory.
The argument has a concept gap. The premise introduces 'extra spatial dimensions', but the conclusion relies on the rule for 'purely theoretical entities'.
To guarantee the conclusion, an assumption must bridge this vocabulary gap by explicitly classifying these dimensions as theoretical entities.
2
Analyze the public policy argument regarding housing reform.
The argument proves the reform 'stimulates the construction sector', but the conclusion leaps to the claim that it will 'alleviate the housing shortage'.
A sufficient assumption must state that the proven intermediate result (stimulating construction) is enough to guarantee the final outcome (alleviating the shortage).
3
Analyze the economic argument regarding monetary policy.
The argument contains a conditional logic flaw. It states that diminishing spending is necessary ('only if') to curb inflation, but then treats it as if it is sufficient to guarantee the curbing of inflation.
The required assumption must fix this flaw by explicitly stating that reducing purchasing activity (diminishing spending) is sufficient to arrest rising prices (curb inflation).
4
Analyze the ethical argument regarding corporate liquidation.
The premise establishes a factual action (prioritizing dividends over security), while the conclusion makes a normative moral judgment ('unethical').
We need a bridge principle that explicitly connects the factual action to the normative judgment, defining that specific prioritization as ethically impermissible.

Key Concept

Identifying the missing logical link or repairing the logical flaw to create a valid deductive argument where the conclusion is entirely guaranteed by the premises.
Question 47Question →

Archaeologist: The abandonment of the thriving ancient settlement of Kelior is generally attributed to a century-long regional drought. However, isotopic analysis of soil strata indicates that less than a decade before the abandonment, Kelior's farmers abruptly transitioned from cultivating teff, a highly drought-resistant grain, to a variety of water-intensive marsh-rice. Therefore, it was actually this ill-advised agricultural pivot, rather than the drought alone, that precipitated the settlement's collapse by engineering a catastrophic famine.

The archaeologist's argument relies on which one of the following assumptions?

Show answer & explanation

Answer: The regional drought was not so extreme that it would have caused a catastrophic famine at Kelior even if the farmers had continued cultivating teff exclusively.

Answer

The assumption that the drought was not severe enough to destroy the drought-resistant teff crops.
In this argument, the author attempts to shift the blame for a historical famine from an external factor (a drought) to an internal factor (an agricultural pivot). To successfully argue that the pivot, 'rather than the drought alone', was the cause, the author must inherently assume that the drought was not independently capable of causing the exact same catastrophic outcome. If the drought would have decimated the highly resistant teff anyway, the farmers' ill-advised pivot to rice was irrelevant to their ultimate fate. Therefore, the argument depends on the assumption that the drought was not extreme enough to destroy the original crops.

Step-by-Step Solution

1
Identify the main conclusion of the argument.
The conclusion is that the agricultural pivot to marsh-rice, rather than the drought alone, precipitated the settlement's collapse by causing a famine.
Understanding the exact causal claim is necessary to evaluate what the author must assume to make this claim.
2
Identify the premises supporting the conclusion.
1. Kelior faced a century-long drought. 2. Shortly before abandonment, farmers switched from drought-resistant teff to water-intensive marsh-rice.
Premises provide the foundation; the assumption must bridge the gap between these facts and the causal conclusion.
3
Anticipate alternate explanations (weaknesses) in the causal claim.
What if the drought was incredibly severe—so apocalyptic that no crop, not even the highly resistant teff, could have survived? If that were true, the crop pivot didn't matter; the drought alone caused the famine.
A 'Defender' assumption works by explicitly ruling out a potential weakness or alternate explanation that would destroy the argument.
4
Apply the Negation Technique to the correct option.
Negated correct answer: The drought WAS so extreme it would have caused a famine even if they cultivated teff. This directly contradicts the conclusion that the pivot, rather than the drought alone, caused the famine.
The Negation Test is the definitive proof for a Necessary Assumption question. If negating the choice destroys the argument, it is the correct answer.

Key Concept

Necessary Defender Assumptions in Causal Arguments
Question 48Question →

Researchers recently observed that office workers who regularly consume green tea report experiencing significantly lower levels of daily stress than those who do not. Furthermore, among the workers observed, those who consume the greatest amount of green tea report the lowest stress levels. The researchers conclude that the antioxidants present in green tea act directly on the nervous system to reduce stress.

Which one of the following is an assumption on which the researchers' argument depends?

Show answer & explanation

Answer: An office worker's level of daily stress does not dictate their likelihood of consuming green tea.

Answer

The argument depends on the assumption that an office worker's level of daily stress does not dictate their likelihood of consuming green tea (ruling out reverse causation).
The correct answer rules out the possibility of reverse causation. The argument observes a correlation between green tea and lower stress, and concludes that the tea causes the lower stress. For this causal claim to be valid, it must be true that the causal arrow does not point the other way. If it were true that having low stress naturally leads people to drink green tea, the conclusion would fall apart. Therefore, the argument implicitly assumes that an individual's stress level is not what dictates their tea consumption.

Step-by-Step Solution

1
Analyze the argument's structure to identify the premises and conclusion.
Premise: There is a dose-dependent correlation between green tea consumption and lower stress. Conclusion: Antioxidants in green tea directly reduce stress.
Deconstructing the argument is the first step in identifying the logical gap.
2
Identify the logical gap between the premises and the conclusion.
The premises only establish a correlation, but the conclusion claims a specific causal relationship (A causes B).
Causal conclusions drawn from correlational data always contain logical gaps, as there are alternative explanations for the correlation.
3
Determine what type of assumption is needed to bridge this gap.
A necessary assumption is required. This often takes the form of a 'Defender' assumption that rules out an alternate cause or reverse causation.
The question stem asks for an assumption the argument 'depends' on.
4
Evaluate the options using the Negation Test.
Negating the correct option yields: 'An office worker's level of daily stress DOES dictate their likelihood of consuming green tea.' If low stress causes people to drink tea, the conclusion that tea causes low stress is undermined.
The Negation Test is the definitive way to prove a necessary assumption. If the negated option destroys the argument, it is the correct answer.

Key Concept

Ruling out reverse causation in causal arguments
Question 49Question →

Match each causal argument below to the specific category of necessary assumption it fundamentally relies upon.

Click a left item, then click its matching right item

Items

Following a new city public relations campaign, local tourism rose by 15 percent. The mayor concluded that the campaign caused the increase in tourism.
A study shows that individuals who exercise regularly are more likely to report feeling happy. Researchers conclude that exercise causes an increase in happiness.
Data reveals that months with high ice cream sales also experience high drowning rates. A report concludes that eating ice cream increases the risk of drowning.
Patients taking a new experimental supplement recovered from the flu in exactly five days. The creators claim that the supplement cures the flu.

Matches

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Answer

The PR campaign argument matches with eliminating alternate causes. The exercise argument matches with eliminating reverse causality. The ice cream argument matches with eliminating a third-variable common cause. The flu supplement argument matches with establishing a control baseline.
Each argument precisely demonstrates a classic causal reasoning gap. The PR campaign relies on eliminating alternate causes for a subsequent event. The exercise study relies on eliminating reverse causality. The ice cream correlation relies on eliminating a third shared cause. The flu remedy relies on assuming the effect wouldn't occur naturally.

Step-by-Step Solution

1
Analyze the public relations argument to identify its specific logical leap.
The argument assumes that because the campaign preceded the tourism increase, it caused it. It matches the assumption that no other independent factor caused the effect.
Chronological arguments typically require ruling out alternate events occurring at the same time.
2
Analyze the exercise and happiness argument.
The argument jumps from a correlation between two states of being to a specific causal direction. It matches the assumption that the effect (happiness) did not cause the cause (exercise).
When two traits exist simultaneously, the causal relationship could logically go in either direction, requiring the assumption that reverse causality is false.
3
Analyze the ice cream and drowning argument.
The argument connects two unrelated events occurring at the same time. It matches the assumption that a third variable does not cause both.
When two entirely distinct phenomena correlate, a common cause (like weather) is the most likely alternative explanation that must be assumed away.
4
Analyze the flu supplement argument.
The argument notes an outcome after an action without a comparison. It matches the assumption that the flu would not have resolved naturally in the same timeframe.
Arguments about medical or temporal interventions must assume a baseline where the intervention's absence leads to a different outcome.

Key Concept

Assumptions in Causal Arguments
Question 50Question →

Analyze the following flawed arguments, all of which share a common set of variables regarding commercial development. Match each argument with the specific missing assumption required to make its conclusion logically follow.

Click a left item, then click its matching right item

Items

Any commercial development approved by the Planning Commission passes the mandatory environmental audit. It logically follows that any development approved by the Planning Commission is guaranteed to receive a municipal tax subsidy.
A commercial development is awarded a municipal tax subsidy provided that it incorporates extensive green spaces. Therefore, any development that incorporates extensive green spaces will undoubtedly be approved by the Planning Commission.
The Planning Commission approves a commercial development if that development receives a municipal tax subsidy. Consequently, no commercial development can receive a municipal tax subsidy unless it incorporates extensive green spaces.
Any commercial development that passes the mandatory environmental audit is awarded a municipal tax subsidy. From this, one can conclude that a development will receive a municipal tax subsidy whenever it incorporates extensive green spaces.

Matches

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Answer

Argument 1 pairs with the assumption that failing to receive a subsidy implies failing the audit. Argument 2 pairs with the assumption that a subsidy requires Planning Commission approval. Argument 3 pairs with the assumption that approval guarantees green spaces. Argument 4 pairs with the assumption that incorporating green spaces requires passing the audit.
Each argument contains a logical gap between its premises and its conclusion. By translating the statements into formal conditional logic, we can identify the exact missing premise required for the conclusion to be drawn validly. Argument 1 requires E -> T, which matches the contrapositive statement ~T -> ~E. Argument 2 requires T -> P, which matches the 'unless' statement translating to ~P -> ~T. Argument 3 requires P -> G, which matches the 'guarantees' statement. Argument 4 requires G -> E, which matches the 'only if' statement.

Step-by-Step Solution

1
Define variables for the four recurring elements across all arguments.
Let P = Approved by Planning Commission, E = Passes environmental audit, T = Receives tax subsidy, G = Incorporates green spaces.
Standardizing variables prevents confusion since all arguments use the exact same vocabulary but in different logical structures.
2
Determine the formal logic gap for Argument 1 and find the matching assumption.
Premise: P -> E. Conclusion: P -> T. The gap is E -> T. The assumption 'Failing to receive... subsidy (~T) implies... did not pass... audit (~E)' is the contrapositive of E -> T.
A valid assumption must logically bridge the stated premise to the derived conclusion.
3
Determine the formal logic gap for Argument 2 and find the matching assumption.
Premise: G -> T (from 'T provided that G'). Conclusion: G -> P. The gap is T -> P. The assumption 'cannot receive... subsidy (~T) unless approved (P)' translates to ~P -> ~T, or T -> P.
The 'unless' indicator translates to a necessary condition. 'A unless B' means 'If not B, then A' (~B -> A).
4
Determine the formal logic gap for Argument 3 and find the matching assumption.
Premise: T -> P. Conclusion: T -> G (from 'no T unless G'). The gap is P -> G. The assumption 'Approval guarantees... green spaces' translates directly to P -> G.
To connect the sufficient condition (T) to the new necessary condition (G), the intermediate term (P) must guarantee (G).
5
Determine the formal logic gap for Argument 4 and find the matching assumption.
Premise: E -> T. Conclusion: G -> T (from 'T whenever G'). The gap is G -> E. The assumption 'G only if E' translates directly to G -> E.
The phrase 'only if' introduces a necessary condition, meaning the term before it is the sufficient condition.

Key Concept

Identifying missing conditional links and translating complex conditional indicators (unless, provided that, whenever, implies, only if) into formal logic.
Question 51Question →

Read the argument below and evaluate whether the provided statement functions as a necessary assumption.

Historian: The invention of writing must have been driven by the need to manage the increasingly complex trade networks of early agricultural surpluses, not by the administrative demands of large-scale monumental building projects. The traditional theory favoring monumental architecture as the primary catalyst is decisively refuted by recent excavations at Oruk, which reveal that complex record-keeping systems were fully established centuries before the construction of any such monuments.

Statement: The administrative demands associated with large-scale monumental building projects did not arise centuries before the actual physical construction of such monuments began.

Show answer & explanation

Answer: True

Answer

True. The statement is a necessary assumption.
The correct answer is True because the statement is a necessary assumption required for the argument's logic to hold. The historian concludes that trade networks, rather than monument building, catalyzed the invention of writing. The sole evidence provided is chronological: writing systems were established centuries before any monuments were physically constructed. For this evidence to successfully refute the traditional theory, the historian must assume that the administrative demands of monument building did not precede the actual construction by centuries. We can prove this is necessary using the Negation Technique. If we negate the statement—assuming that the administrative demands did arise centuries before actual construction began, perhaps for long-term resource gathering or site planning—then it is entirely possible that these early administrative demands drove the invention of writing. This destroys the historian's premise that the timeline refutes the traditional theory, which in turn causes the main conclusion to collapse.

Step-by-Step Solution

1
Analyze the structure of the argument.
Conclusion: Trade networks, not monument building, caused the invention of writing. Premise: Writing existed centuries before monument construction began.
Identifying the core logic and identifying any leaps in reasoning is the first step.
2
Identify the logical gap.
The historian assumes that the timeline of physical construction directly mirrors the timeline of its administrative demands.
To refute a causal relationship based on a timeline, the cause itself must not predate the effect.
3
Apply the Negation Technique to the statement.
Negated statement: The administrative demands of monument building DID arise centuries before actual construction began.
The Negation Technique is the definitive test for a necessary assumption.
4
Evaluate the impact of the negated statement.
If the demands arose centuries earlier, they could have caused the invention of writing. The traditional theory survives, destroying the argument's conclusion.
If the logical negation destroys the argument, the original statement is a strictly necessary assumption.

Key Concept

Identifying Necessary Assumptions using the Negation Technique on 'Defender' assumptions that rule out alternate timelines.
Estimated Time:2m 0s
Question 52Question →

When evaluating arguments on the LSAT, determining whether an assumption is strictly necessary requires properly applying the Negation Technique. This involves identifying the precise logical contradictory of a candidate statement. Match each candidate assumption regarding workforce productivity on the left with its precise logical negation on the right.

Click a left item, then click its matching right item

Items

Any systemic transition to a compressed four-day workweek will inherently precipitate a sustained increase in aggregate workforce productivity.
Only a systemic transition to a compressed four-day workweek possesses the capacity to precipitate a sustained increase in aggregate workforce productivity.
Most systemic transitions to a compressed four-day workweek will precipitate a sustained increase in aggregate workforce productivity.
At least some systemic transitions to a compressed four-day workweek will precipitate a sustained increase in aggregate workforce productivity.

Matches

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Answer

The correct pairings isolate the specific quantifiers ('Any', 'Only', 'Most', 'Some') and match them with their precise logical contradictories.
Applying the Negation Technique effectively requires understanding the mathematical boundaries of logical quantifiers. 'Any' (100%) is contradicted by 'Not All' (<100%). 'Only' establishes a mandatory necessary condition, which is logically negated by showing alternatives exist. 'Most' (>50%) is negated by its mathematical complement (≤50%). 'Some' (>0%) is negated by 'None' (0%).

Step-by-Step Solution

1
Analyze the quantifier in 'Any systemic transition...'
The statement asserts 'All X are Y'. The logical contradictory is 'At least one X is not Y', which matches the option stating 'At least one... will fail'.
Negating a universal statement requires showing it is not absolute, rather than proposing its polar opposite ('None').
2
Analyze the restrictive conditional 'Only a systemic transition...'
The statement asserts 'No non-X is Y'. The contradictory is 'At least one non-X is Y', which matches the option stating the outcome 'could be precipitated by structural changes other than' the transition.
The negation of a necessary condition demonstrates that the necessary requirement could be bypassed, meaning the result can be achieved through alternative means.
3
Analyze the majority quantifier in 'Most systemic transitions...'
The statement asserts 'More than 50% of X are Y'. The contradictory encompasses the remaining mathematical space: '50% or fewer', matching the 'Half or fewer' option.
A common logical flaw is negating 'Most' with 'None' or 'Some are not', but the true logical contradictory splits the 100% distribution precisely at the 50% threshold.
4
Analyze the existential quantifier in 'At least some systemic transitions...'
The statement asserts 'At least one X is Y' (1% to 100%). The contradictory must cover the remaining space (0%), which matches 'No systemic transition...'.
If it is false that 'some' (even one) exist, then it must logically follow that 'none' exist.

Key Concept

Logical Quantifier Negation
Estimated Time:2m 0s
Question 53Question →

Biologist: The prehistoric canid *Aetocyon* must have lived and hunted in large social groups. The recent discovery of fossilized *Aetocyon* reveals that these animals had highly specialized jaw structures adapted exclusively for crushing large bones. In the modern world, bone-crushing predators such as spotted hyenas hunt in large, coordinated packs in order to take down large prey.

Which of the following are necessary assumptions on which the biologist's argument depends? (Select all that apply.)

Select all that apply

Show answer & explanation

Answer: *Aetocyon* did not rely predominantly on scavenging the kills of other animals to obtain the large bones it crushed.; A single *Aetocyon* was physically incapable of taking down the large prey animals from which the crushed bones were derived.

Answer

The correct statements are that the animal did not rely predominantly on scavenging, and that a single individual was incapable of taking down the large prey.
The biologist argues that because modern bone-crushing predators hunt in large packs to take down large prey, the prehistoric canid must have done the same. This reasoning relies on bridging two distinct logical gaps. First, it assumes the canid acquired large bones by hunting rather than scavenging. By applying the Negation Technique, if the animal DID rely predominantly on scavenging, the need for a large pack to take down prey is eliminated, destroying the argument. Second, the argument assumes a single animal could not take down large prey on its own. If one individual WAS physically capable of taking down large prey alone, there would be no requirement for them to hunt in large, coordinated packs, which also causes the conclusion to collapse.

Step-by-Step Solution

1
Deconstruct the argument into its core components.
Conclusion: The prehistoric animal must have lived and hunted in large social groups. Premises: It had bone-crushing jaws; modern bone-crushers hunt in large packs to take down large prey.
Identifying the exact conclusion and the supporting evidence is necessary to locate the logical gaps.
2
Identify the unstated logical leaps.
The argument leaps from 'bone-crushing jaws' to 'hunting in packs'. It assumes the animal actually hunted its own large prey instead of scavenging, and that the prey was too large for a solitary hunter.
A necessary assumption is an unstated premise that bridges a gap and must be true for the conclusion to stand.
3
Apply the Negation Technique to test the options.
Negating the correct statements causes the argument to fail. If the animal scavenged predominantly, or if it could hunt large prey alone, the conclusion that it MUST have hunted in large packs is destroyed.
The Negation Technique definitively proves whether an assumption is logically required by the argument.

Key Concept

Identifying Necessary Assumptions using the Negation Technique
Question 54Question →

Ethicist: A moral theory is practically viable only if it can be consistently applied by ordinary individuals in their daily lives. Because Utilitarianism requires a level of cognitive effort that far exceeds the psychological capacity of average humans, it is impossible for ordinary individuals to consistently apply it. Consequently, Utilitarianism cannot serve as the foundational moral framework for a functioning society.

Which one of the following is an assumption on which the ethicist's argument depends?

Show answer & explanation

Answer: In order to serve as the foundational moral framework for a functioning society, a moral theory must be practically viable.

Answer

The statement asserting that a moral theory must be practically viable in order to serve as the foundational framework for a functioning society.
The ethicist's argument traces a path from the cognitive demands of Utilitarianism to the conclusion that it is not practically viable. However, the final conclusion introduces an entirely new claim: that Utilitarianism cannot be the 'foundational moral framework for a functioning society.' Because this concept appears nowhere in the premises, there is a logical gap. The author must be assuming that lacking practical viability automatically disqualifies a theory from being a foundational framework. The correct answer explicitly provides this exact link by stating that practical viability is a necessary prerequisite for serving as a foundational framework.

Step-by-Step Solution

1
Analyze the logical structure of the premises.
Premise 1 establishes: Viable → Consistently Applied. Premise 2 establishes: Utilitarianism → Exceeds Capacity → NOT Consistently Applied.
Deconstructing the text into formal logic reveals the exact endpoints of the evidence provided.
2
Determine the intermediate inference supported by the premises.
Since Utilitarianism cannot be consistently applied (denying the necessary condition for viability in Premise 1), it can be inferred that Utilitarianism is NOT practically viable.
Applying the contrapositive of Premise 1 (NOT Consistently Applied → NOT Viable) to Utilitarianism completes the premise chain.
3
Identify the main conclusion and isolate the rogue element.
The conclusion claims Utilitarianism cannot serve as a 'foundational moral framework for a functioning society.' This introduces a completely new concept not mentioned in the premises.
Finding terms in the conclusion that do not appear in the premises pinpoints the exact location of the logical gap.
4
Formulate the required bridging assumption (Supporter).
The assumption must connect the intermediate inference (NOT practically viable) to the conclusion (NOT a foundational framework). Thus: If a theory is NOT practically viable, it is NOT a foundational framework (or, contrapositively, Foundational Framework → Practically Viable).
A Supporter Assumption must syntactically link the established evidence to the unsupported new element in the conclusion.
5
Apply the Negation Test to verify the correct option.
Negating the correct option yields: 'A moral theory does NOT need to be practically viable to serve as a foundational framework.' If true, the fact that Utilitarianism is not viable no longer prevents it from being a framework, destroying the conclusion.
The Negation Test definitively proves whether an assumption is logically necessary for the argument to survive.

Key Concept

Bridging Gap (Supporter) Assumptions in Formal Logic Chains
Question 55Question →

Match each logical reasoning stimulus with the necessary supporter assumption required to logically bridge the conceptual gap between its premises and its conclusion.

Click a left item, then click its matching right item

Items

A scientific theory is robust only if it withstands relentless falsification attempts. Any theory that relies on untestable metaphysical postulates inherently evades such attempts. Thus, the String Landscape model cannot be considered robust.
In civil litigation, punitive damages are warranted if and only if the defendant's conduct demonstrates malicious intent. Negligence arises from a failure of care rather than a desire to cause harm. Therefore, corporations responsible for large-scale environmental disasters should rarely be subjected to punitive damages.
An architectural design achieves timelessness strictly when it successfully harmonizes with its surrounding natural topography. Post-modernist structures deliberately impose stark geometric contrasts against their environments. Consequently, no purely post-modernist civic center will ever be universally admired by future generations.
To consolidate a short-term memory into long-term storage, the hippocampus must undergo uninterrupted protein synthesis during early deep sleep. Pharmaceutical interventions that aggressively suppress cortisol release invariably disrupt this specific sleep phase. Thus, patients taking the anti-anxiety drug 'CortiBlock' will likely experience severe deficits in forming new long-term memories.

Matches

Show answer & explanation

Answer

Each stimulus contains a logical gap between established premise frameworks and a 'rogue' element introduced only in the conclusion. The correct matches provide the exact missing linkages required to make the conclusions logically valid.
Each correct pairing successfully identifies the new, unsupported concept introduced in the conclusion of the stimulus and formally links it back to the conditions established in the premises, satisfying the strict requirements of a Supporter Assumption.

Step-by-Step Solution

1
Analyze the scientific theory stimulus for rogue elements.
Premises link 'untestable metaphysical postulates' to 'not robust'. Conclusion links 'String Landscape model' to 'not robust'.
Identifying the gap reveals that the String Landscape model must be connected to untestable metaphysical postulates.
2
Analyze the civil litigation stimulus for missing logical connections.
Premises link 'punitive damages' to 'malicious intent'. Conclusion asserts 'corporate environmental disasters' rarely warrant punitive damages.
To justify the conclusion, corporate environmental disasters must be classified as lacking malicious intent (i.e., driven by a failure of care).
3
Analyze the architectural design stimulus's conditional chains.
Premises prove post-modernist structures are not timeless. Conclusion claims they won't be universally admired.
The unstated assumption must bridge 'not timeless' to 'not universally admired'. The contrapositive statement matches this perfectly.
4
Analyze the neurobiology stimulus to connect the specific intervention to the general mechanism.
Premises establish that suppressing cortisol prevents memory consolidation. Conclusion claims CortiBlock prevents memory consolidation.
The argument assumes CortiBlock functions by aggressively suppressing cortisol.

Key Concept

Bridging Gap (Supporter) Assumptions
Question 56Question →

Paleontologist: Confidently establishing the basal metabolic rate of any extinct dinosaur species requires researchers to analyze the isotopic composition of its fossilized tooth enamel. The recently excavated skeletal remains of the Tectodon, however, were unearthed exclusively from the remnants of highly acidic ancient peat bogs. Consequently, despite having complete skeletons, researchers will be unable to confidently establish the basal metabolic rate of the Tectodon.

The paleontologist's argument depends on assuming which one of the following?

Show answer & explanation

Answer: Fossilized tooth enamel recovered from highly acidic ancient peat bogs does not retain an analyzable isotopic composition.

Answer

The correct answer is the statement that fossilized tooth enamel recovered from highly acidic ancient peat bogs does not retain an analyzable isotopic composition.
The argument exhibits a clear logical gap: it jumps from the fact that the fossils were found in highly acidic peat bogs to the conclusion that researchers cannot analyze the isotopic composition of their tooth enamel. To make this leap, the paleontologist must assume that the acidic environment of the bogs somehow prevents or ruins this specific isotopic analysis. This option explicitly bridges that gap. Applying the Negation Test confirms this: if tooth enamel from highly acidic bogs DOES retain an analyzable isotopic composition, then the sole reason given for being unable to determine the Tectodon's metabolic rate vanishes, causing the argument's logic to collapse.

Step-by-Step Solution

1
Identify the conclusion of the argument.
Researchers will be unable to confidently establish the basal metabolic rate of the Tectodon.
This is the final claim the paleontologist is trying to prove, signaled by the word 'Consequently'.
2
Identify the premises supporting this conclusion.
Premise 1: Establishing metabolic rate requires analyzing the isotopic composition of tooth enamel. Premise 2: Tectodon fossils were found exclusively in highly acidic ancient peat bogs.
These statements provide the factual foundation and constraints for the argument.
3
Locate the conceptual gap between the premises and the conclusion.
The premises introduce 'highly acidic ancient peat bogs', but the conclusion depends on the inability to 'analyze the isotopic composition of its fossilized tooth enamel'. The argument assumes these specific bogs prevent this specific analysis.
A valid supporter assumption must explicitly connect the new or rogue elements in the premises to those in the conclusion.
4
Apply the Negation Test to the potential correct option to verify it is logically necessary.
If fossils from highly acidic ancient peat bogs DO retain analyzable isotopic compositions, the paleontologist's conclusion that researchers will be 'unable' to establish the metabolic rate falls apart.
A necessary assumption is one that, if proven false, destroys the logical validity of the argument.

Key Concept

Bridging Conceptual Gaps (Supporter Assumptions) and the Negation Test
Question 57Question →

Sociologist: A comprehensive ten-year study tracked adolescents and their video gaming habits. The researchers found that adolescents who predominantly played cooperative multiplayer video games exhibited significantly higher scores on standardized assessments of real-world conflict resolution than adolescents who predominantly played competitive single-player games. Based on these findings, we can safely conclude that engaging in cooperative multiplayer gaming actively fosters and enhances a teenager's ability to resolve interpersonal conflicts.

Which one of the following is an assumption on which the sociologist's argument depends?

Show answer & explanation

Answer: Adolescents who already possess an inherent aptitude for conflict resolution are not significantly more likely to choose cooperative multiplayer games over competitive ones.

Answer

The correct answer is the one stating that adolescents with preexisting conflict resolution skills are not disproportionately drawn to cooperative games.
The sociologist commits a classic correlation-to-causation flaw by assuming that because cooperative gaming and conflict resolution skills appear together, the gaming must cause the skills. A critical alternate explanation for this correlation is self-selection bias (reverse causality): perhaps teenagers who are naturally empathetic and good at resolving conflicts simply prefer cooperative games. For the sociologist's conclusion to stand, this alternate explanation must be false. The correct option explicitly rules out this alternate explanation, defending the original causal claim. When subjected to the Negation Test, the argument collapses, proving this assumption is logically necessary.

Step-by-Step Solution

1
Analyze the argument's structure to identify the premise and conclusion.
Premise: There is a correlation between playing cooperative games and having higher conflict resolution scores. Conclusion: Playing cooperative games causes an enhancement in conflict resolution skills.
Identifying the shift from a correlational premise to a causal conclusion is essential for spotting the logical gap.
2
Determine the type of assumption required by the question stem.
The phrase 'depends on' indicates a Necessary Assumption question.
Necessary assumptions must be true for the argument to survive. We must use the Negation Test to verify the correct answer.
3
Identify potential flaws or alternate explanations for the causal conclusion.
The correlation could be caused by reverse causality (selection bias): teens who are already good at resolving conflicts naturally prefer to play cooperative games.
In causal arguments, the author always assumes there are no alternate causes, no reverse causality, and no third-variable confounders.
4
Evaluate the choices looking for a 'Defender' assumption that rules out an alternate explanation, and apply the Negation Test to the strongest candidate.
Negating the correct option yields: 'Adolescents who already possess an inherent aptitude for conflict resolution ARE significantly more likely to choose cooperative multiplayer games.'
If this negated version is true, the conclusion falls apart because the gaming didn't cause the skill; the skill caused the choice of gaming. Therefore, the original statement is strictly necessary.

Key Concept

Defender Assumptions in Causal Arguments
Question 58Question →

If a scientific paradigm is fundamentally unfalsifiable, it cannot serve as the foundation for a robust empirical research program. A paradigm is fundamentally unfalsifiable only if its core propositions are completely insulated from observable phenomena. Dr. Aris's new framework of consciousness features core propositions that are deeply intertwined with observable neurological phenomena. It follows that Dr. Aris's framework can serve as the foundation for a robust empirical research program.

Which one of the following, if assumed, enables the conclusion to be properly drawn?

Show answer & explanation

Answer: Any scientific paradigm that is not fundamentally unfalsifiable is capable of serving as the foundation for a robust empirical research program.

Answer

The correct assumption is that any scientific paradigm that is not fundamentally unfalsifiable is capable of serving as the foundation for a robust empirical research program.
The correct answer perfectly bridges the logical gap in the argument. The premises establish that Dr. Aris's framework is not completely insulated (~CI), which proves it is not fundamentally unfalsifiable (~FU). However, the author concludes that the framework will therefore serve as a robust foundation (RF). The author has committed a flaw by assuming that just because unfalsifiable theories fail, falsifiable ones will succeed. The correct answer choice explicitly provides this exact missing rule (~FU → RF), allowing the conclusion to be drawn with absolute logical certainty.

Step-by-Step Solution

1
Translate the first premise into formal conditional logic.
Fundamentally Unfalsifiable (FU) → NOT a Robust Foundation (~RF). The contrapositive is: RF → ~FU.
To establish the initial conditional relationship provided by the argument.
2
Translate the second premise into formal conditional logic.
Fundamentally Unfalsifiable (FU) → Completely Insulated (CI). The contrapositive is: NOT Completely Insulated (~CI) → ~FU.
To understand the necessary condition for a paradigm being unfalsifiable, triggered by the phrase 'only if'.
3
Evaluate the argument's factual application to Dr. Aris's framework.
The framework's propositions are intertwined with observable phenomena, meaning it is NOT completely insulated (~CI). Following the chain from Step 2 (~CI → ~FU), we deduce that Dr. Aris's framework is NOT fundamentally unfalsifiable (~FU).
To determine what is logically proven about this specific framework based strictly on the given premises.
4
Identify the logical gap between the deduced facts and the final conclusion.
The premises strictly prove that Dr. Aris's framework is ~FU. The author's conclusion is that the framework is RF. Thus, the author erroneously assumes that ~FU → RF (an illegal reversal of the first premise).
Identifying the author's logical leap reveals exactly what sufficient assumption is missing.
5
Formulate the missing sufficient assumption.
We must explicitly add the missing link: ~FU → RF (If a paradigm is not fundamentally unfalsifiable, it can serve as a robust foundation).
A sufficient assumption must perfectly bridge the gap between the proven evidence and the final conclusion.

Key Concept

Bridging conditional logic gaps by identifying illegal reversals and supplying the missing sufficient condition.
Question 59Question →

Ten years ago, the national government introduced a substantial tax on plastic packaging used by food manufacturers. Since the tax was implemented, the volume of plastic waste deposited in the nation's municipal landfills has decreased by 30 percent. Economists assert that the tax achieved its intended goal, concluding that the financial penalty forced food manufacturers to switch to biodegradable packaging alternatives, thereby reducing the amount of plastic waste generated.

Which one of the following is an assumption required by the economists' argument?

Show answer & explanation

Answer: The nation did not substantially increase the proportion of its plastic waste that is diverted from municipal landfills to recycling programs or export markets over the past ten years.

Answer

The assumption that the nation did not substantially increase the proportion of plastic waste diverted to recycling or export markets.
The argument leaps from a decrease in plastic waste at municipal landfills to the conclusion that less plastic waste is being generated overall due to a switch to biodegradable packaging. For this causal conclusion to hold, the economists must assume that the missing plastic waste didn't simply go to a different destination. The correct answer acts as a 'Defender' assumption by ruling out the alternative explanation that the plastic waste was merely diverted to recycling centers or exported. If we apply the Negation Technique and assume the nation DID substantially increase its diversion of plastic waste to recycling or exports, it completely explains the 30 percent drop in landfills. This destroys the argument's claim that the drop was due to a reduction in generated waste.

Step-by-Step Solution

1
Analyze the stimulus to identify the premises and the main conclusion.
Premise: Landfill plastic waste dropped by 30 percent after a packaging tax was implemented. Conclusion: The tax forced food manufacturers to switch to biodegradable packaging, reducing generated plastic waste.
Understanding the exact scope of the evidence and the conclusion is required to spot logical gaps.
2
Identify the logical gap or flaw in the argument.
The argument assumes that a reduction in 'landfilled' waste equals a reduction in 'generated' waste. It ignores the possibility that the waste is still being generated but is going somewhere else.
Causal conclusions based on correlational evidence are vulnerable to alternative causes or explanations.
3
Evaluate the options using the Negation Technique to find the necessary Defender assumption.
Negating the correct option reveals that if waste diversion (recycling/export) increased substantially, it would perfectly explain the landfill drop without needing the manufacturers to switch packaging. Thus, ruling out this alternative is logically necessary.
A necessary assumption is a statement that must be true for the conclusion to hold; if its negation ruins the argument, it is the correct answer.

Key Concept

Ruling Out Alternate Explanations (Defender Assumptions)
Question 60Question →

Analyze each of the following logical arguments. Match each argument to the specific sufficient assumption that, if added to its premises, strictly and logically guarantees the truth of its conclusion.

Click a left item, then click its matching right item

Items

The new software update improves battery life. Any software update that improves battery life is guaranteed to be widely downloaded. Therefore, the new software update will definitely increase the tech company's revenue.
The mayor's zoning proposal will reduce urban sprawl. However, the city council will support a proposal only if it does not harm the local economy. Since the mayor's zoning proposal will not harm the local economy, it will surely be supported by the city council.
A daily diet high in leafy greens provides a person with essential B-vitamins. We know that vitamin deficiencies often lead to chronic fatigue. Therefore, anyone who eats a diet high in leafy greens will not experience chronic fatigue.
Historically, civilizations that developed advanced writing systems experienced rapid technological growth. The newly discovered ancient civilization in the Valley of Lorn experienced rapid technological growth. Thus, the civilization in the Valley of Lorn must have developed an advanced writing system.

Matches

Show answer & explanation

Answer

Each argument requires a distinct formal logic assumption to guarantee its conclusion: linking a new term in the conclusion (Left 1 to Right 1), reversing a necessary condition to make it sufficient (Left 2 to Right 2), negating a condition to form a direct sufficient link (Left 3 to Right 3), and establishing a necessary condition for a historical outcome (Left 4 to Right 4).
Each matched assumption provides the exact logical bridge required to make the corresponding conclusion 100% valid, effectively transforming flawed or incomplete deductive arguments into airtight formal logic.

Step-by-Step Solution

1
Analyze the first argument to identify the gap between the established premises and the main conclusion.
The premises prove the update will be 'widely downloaded,' but the conclusion claims it will 'increase revenue.'
Identifying the 'new' term in the conclusion reveals exactly what the sufficient assumption must connect.
2
Evaluate the conditional structure of the second argument regarding the mayor's proposal.
The premise gives 'Support -> Not Harm Economy'. The argument applies 'Not Harm Economy' to conclude 'Support'.
This is a classic flawed reversal. To make the argument logically valid, the relationship must be assumed in the other direction: 'Not Harm Economy -> Support'.
3
Identify the flawed reasoning in the third argument about leafy greens.
The premise states 'No Vitamins -> Fatigue'. The conclusion assumes 'Vitamins -> No Fatigue'.
This is a flawed negation. A sufficient assumption must bridge this by explicitly stating 'Vitamins -> No Fatigue'.
4
Diagram the formal logic in the fourth argument regarding the ancient civilization.
Premise: 'Writing -> Tech Growth'. Conclusion applied to Lorn: 'Tech Growth -> Writing'.
The argument improperly treats a sufficient condition as a necessary one. The assumption must state that writing is the 'only' way (a necessary condition) to achieve rapid technological growth.

Key Concept

Identifying Formal Logic Gaps and Sufficient Assumptions
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