Logical Reasoning

666 questions

Question 661Question →

Below are five short arguments concerning the proposed Arcadia transit expansion. Each argument is logically incomplete because it commits a formal reasoning error or lacks a crucial premise. Match each incomplete argument to the specific sufficient assumption that perfectly bridges its logical gap.

Click a left item, then click its matching right item

Items

Argument 1: A municipal transit plan will secure federal funding only if it increases daily ridership. The Arcadia proposal centers on implementing automated ticketing, a measure that guarantees an increase in daily ridership. Therefore, the Arcadia proposal will successfully secure federal funding.
Argument 2: If a transit plan implements automated ticketing, it will eliminate toll jobs. Furthermore, eliminating toll jobs is a necessary condition for reducing carbon emissions. The Arcadia proposal will definitely eliminate toll jobs. Therefore, the Arcadia proposal involves implementing automated ticketing.
Argument 3: In order to reduce carbon emissions, a transit system must secure federal funding. The Arcadia proposal focuses on implementing automated ticketing, which unfortunately disqualifies it from securing federal funding. Therefore, the Arcadia proposal will eliminate toll jobs.
Argument 4: Most transit plans that increase daily ridership also succeed in reducing carbon emissions. By securing federal funding, the Arcadia proposal ensures that it will increase daily ridership. Therefore, the Arcadia proposal will ultimately implement automated ticketing.
Argument 5: Any transit plan that eliminates toll jobs will fail to secure federal funding unless it also increases daily ridership. The Arcadia proposal eliminates toll jobs but successfully increases daily ridership. Therefore, the Arcadia proposal will succeed in reducing carbon emissions.

Matches

Show answer & explanation

Answer

Argument 1 matches with the ridership-to-funding assumption. Argument 2 matches with the job-elimination-to-ticketing assumption. Argument 3 matches with the failed-funding-to-job-elimination assumption. Argument 4 matches with the ridership-to-ticketing assumption. Argument 5 matches with the combined job-elimination-and-ridership-to-emissions assumption.
Each correct assumption perfectly completes the deductive bridge by converting the argument's logical gap into a valid modus ponens deduction. By mapping the premises as conditional statements, we isolate the exact trigger needed to force the conclusion to be true.

Step-by-Step Solution

1
Identify the pool of repeating concepts across all arguments
Five concepts are used interchangeably: Automated Ticketing, Federal Funding, Daily Ridership, Toll Jobs, and Carbon Emissions.
Because all arguments use the same vocabulary, keyword matching will fail. Formal logic mapping is required.
2
Diagram the formal logic of Argument 1 and identify the gap
Premises: Funding -> Ridership; Ticketing -> Ridership. Fact: Arcadia has Ticketing (thus Ridership). Conclusion: Arcadia has Funding. Gap: Ridership -> Funding.
To fix the sufficient/necessary confusion, we must make the necessary condition sufficient.
3
Diagram Argument 2 and identify the gap
Premises: Ticketing -> Toll Jobs; Carbon -> Toll Jobs. Fact: Arcadia has Toll Jobs. Conclusion: Arcadia has Ticketing. Gap: Toll Jobs -> Ticketing.
To fix the Mistaken Reversal, we must connect the established fact (eliminating toll jobs) to the conclusion.
4
Diagram Argument 3 and identify the gap
Premises: Carbon -> Funding; Ticketing -> ~Funding. Fact: Arcadia has Ticketing (thus ~Funding). Conclusion: Arcadia eliminates Toll Jobs. Gap: ~Funding -> Toll Jobs.
We must bridge the intermediate deduction (~Funding) to the new term in the conclusion (Toll Jobs).
5
Diagram Argument 4 and identify the gap
Premises: Ridership -most-> Carbon; Funding -> Ridership. Fact: Arcadia has Funding (thus Ridership). Conclusion: Arcadia has Ticketing. Gap: Ridership -> Ticketing.
We must link the proven intermediate step (Ridership) to the conclusion (Ticketing).
6
Diagram Argument 5 and identify the gap
Fact: Arcadia eliminates Toll Jobs AND increases Ridership. Conclusion: Arcadia reduces Carbon. Gap: (Toll Jobs + Ridership) -> Carbon.
We must directly connect the compound factual evidence to the new conclusion.

Key Concept

Sufficient Assumptions via Formal Logic Mapping
Estimated Time:3m 30s
Question 662Question →

Legal scholar: A judicial ruling cannot be considered legally definitive unless it relies upon settled case law or explicitly overturns prior interpretive frameworks. We know that any ruling explicitly overturning prior interpretive frameworks inevitably destabilizes market expectations. The recent appellate decision regarding digital asset property rights clearly did not destabilize market expectations. Therefore, the recent appellate decision cannot be considered legally definitive.

The conclusion drawn by the legal scholar follows logically if which one of the following is assumed?

Show answer & explanation

Answer: The recent appellate decision regarding digital asset property rights did not rely upon settled case law.

Answer

The recent appellate decision regarding digital asset property rights did not rely upon settled case law.
The argument's first sentence establishes that for a ruling to be legally definitive, it must satisfy at least one of two conditions: relying on settled case law OR overturning prior frameworks. The subsequent premises establish that overturning prior frameworks always destabilizes markets, and that this specific decision did NOT destabilize markets. From this, we deduce the decision did NOT overturn prior frameworks. To conclude that the decision is definitely NOT legally definitive, we must eliminate the only other path to being definitive: relying on settled case law. The correct answer explicitly states that the decision did not rely on settled case law, perfectly closing the gap and guaranteeing the conclusion.

Step-by-Step Solution

1
Map the formal logic of the first premise.
Definitive (LD) -> Settled Case Law (SCL) OR Overturns Frameworks (OPIF). The contrapositive is: If NOT SCL AND NOT OPIF -> NOT LD.
Understanding the conditional relationship established by the word 'unless' is required to see what is necessary to prove the conclusion.
2
Map the formal logic of the second and third premises.
OPIF -> Destabilizes Market Expectations (DME). The appellate decision (AppDec) -> NOT DME.
This allows for deductions based on the specific scenario presented.
3
Derive the intermediate conclusion.
Because AppDec -> NOT DME, and OPIF -> DME, we can deduce via contrapositive that AppDec -> NOT OPIF.
Connecting the premises reveals what is already known to be true about the appellate decision.
4
Identify the logical gap to reach the final conclusion.
The final conclusion is AppDec -> NOT LD. To prove NOT LD, we need BOTH NOT SCL and NOT OPIF. We already know AppDec -> NOT OPIF. Therefore, the missing assumption is AppDec -> NOT SCL.
A sufficient assumption must perfectly bridge the gap between the derived premises and the conclusion.

Key Concept

Sufficient Assumption involving Compound Conditionals and Contrapositives
Question 663Question →

Principle: An academic historian is professionally justified in publishing a controversial historical claim based on newly discovered, unauthenticated documents only if the claim challenges a prevailing consensus that was itself established without rigorous primary source documentation, and the historian explicitly acknowledges the unauthenticated status of these documents. Furthermore, even if the preceding conditions are satisfied, the historian is not justified unless the potential value of the new claim to historical discourse outweighs the risk of disseminating historical inaccuracies.

Which one of the following judgments conforms most closely to the principle stated above?

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Answer: Dr. Morell published a controversial claim based on recently discovered, unauthenticated letters. Her claim challenged a prevailing consensus that lacked rigorous primary source backing, and she explicitly acknowledged the unauthenticated status of the letters. However, because the risk of spreading historical inaccuracies far outweighed the potential value of the claim to historical discourse, Morell was not professionally justified in publishing the claim.

Answer

The judgment concluding that Dr. Morell was not professionally justified because the risk of spreading inaccuracies outweighed the value of the claim.
The correct answer perfectly applies the contrapositive of the final condition in the principle. The stimulus states that a historian is 'not justified unless' the potential value outweighs the risk. This translates to: If Justified -> Value > Risk. The contrapositive is: If Value < Risk -> Not Justified. Because the risk of spreading inaccuracies far outweighed the potential value in this scenario, Dr. Morell failed a necessary condition and was validly deemed not justified.

Step-by-Step Solution

1
Identify the logical structure of the principle in the stimulus.
The principle establishes three necessary conditions for an academic historian to be justified in publishing a claim based on unauthenticated documents.
Recognizing conditional indicators like 'only if' and 'not justified unless' is required to map the strict logic of the argument.
2
Map the specific necessary conditions.
Justified -> (1) Challenges unsupported consensus, AND (2) Acknowledges unauthenticated status, AND (3) Value outweighs risk.
Formalizing the logic prevents confusing necessary conditions with sufficient ones.
3
Determine what conclusions can be validly drawn from this structure.
We can only definitively conclude that a historian is NOT justified (if any of the three conditions fail). We can never conclude they ARE justified, because the principle provides no sufficient conditions.
This immediately rules out any option that concludes a historian is justified.
4
Evaluate the options against the valid logical deductions.
The correct option outlines a scenario where condition 3 fails (value did not outweigh risk), leading to the valid contrapositive conclusion that the historian was not justified.
This perfectly matches the formal logic of the stated principle.

Key Concept

Conditional Logic: Necessary vs. Sufficient Conditions and Contrapositives
Question 664Question →

Marine Biologist: For decades, scientists assumed that the intense bioluminescence of phytoplankton in the Vespera Sea during the summer was simply a physiological byproduct of nutrient-rich deep-ocean upwellings. However, new data reveals that nutrient levels in the Vespera Sea are actually significantly lower in the summer than in the spring, a season when phytoplankton exhibit almost no bioluminescence. Therefore, the summer bioluminescence must be an evolved defensive adaptation against the predatory zooplankton that migrate into the sea during the summer, as these specific predators are known to avoid bright light.

Which of the following, if true, most strongly supports the marine biologist's argument?

Show answer & explanation

Answer: The species of predatory zooplankton that inhabit the Vespera Sea during the spring months are actively attracted to light sources.

Answer

The statement that spring zooplankton are actively attracted to light sources.
The argument concludes that summer bioluminescence is an evolved defense against light-avoiding predators. A major vulnerability in this argument is the question of why the phytoplankton do not simply glow year-round. The correct answer resolves this by demonstrating an evolutionary pressure *against* glowing in the spring (spring predators are attracted to light). By proving that the bioluminescence precisely matches the specific, alternating threats of different seasons, this answer eliminates the possibility that the glowing is merely a random occurrence, thereby massively strengthening the adaptation theory.

Step-by-Step Solution

1
Analyze the core argument and identify the conclusion.
Conclusion: Summer bioluminescence is a defensive adaptation against light-avoiding summer zooplankton.
To know what needs to be strengthened, the exact causal claim must be isolated.
2
Identify the premises and the logical gap in the reasoning.
Premise: Summer nutrients are lower than spring nutrients, yet phytoplankton only glow in summer. Gap: The biologist assumes the glow is specifically tailored to the summer predator, without fully accounting for why the phytoplankton don't just glow year-round if it's generally useful.
Understanding what the argument leaves unaddressed reveals the most effective way to strengthen it.
3
Evaluate the options to find one that bridges the gap or rules out an alternative explanation.
The option stating spring zooplankton are attracted to light explains why the phytoplankton actively suppress or lack bioluminescence in the spring.
If bioluminescence would get them eaten in the spring, it proves the behavior is a highly specific evolutionary response to seasonal predatory habits, thereby strongly confirming the biologist's adaptation hypothesis.

Key Concept

Causal Reasoning and Ruling Out Alternatives in Evolutionary Arguments
Question 665Question →

Archaeologist: The sudden abandonment of the Xionian urban centers around 1200 BCE is traditionally attributed to a severe regional drought that devastated crop yields. However, recent excavations reveal that the cities' massive grain silos were entirely full when the population fled. Furthermore, isotopic analysis of skeletal remains from that period shows no evidence of nutritional stress. Since the population was clearly not starving, the civilization's collapse must have been precipitated by a sudden military invasion rather than by environmental factors.

Which one of the following, if true, most strongly supports the archaeologist's argument?

Show answer & explanation

Answer: Geological surveys indicate that the Xionian cities were built directly above massive, easily accessible freshwater aquifers that were immune to surface drought conditions.

Answer

The correct answer is the option stating that Xionian cities were built above massive freshwater aquifers immune to drought conditions.
The author concludes that environmental factors did not cause the collapse solely because there was no evidence of starvation. However, a drought could easily precipitate a collapse through water scarcity (dehydration) rather than food scarcity, which would still leave the grain silos full. This correct answer explicitly rules out the possibility of a water shortage by establishing that the cities had access to immune freshwater aquifers. By eliminating the most plausible alternative environmental threat, it significantly strengthens the conclusion that the collapse was due to non-environmental reasons, such as a military invasion.

Step-by-Step Solution

1
Analyze the argument's structure to isolate the premises and the main conclusion.
Conclusion: A sudden military invasion, not environmental factors, caused the collapse. Premises: The grain silos were full, and skeletons showed no nutritional stress.
Identifying the exact boundaries of the author's claim is required to find where the logic is vulnerable.
2
Identify the logical gap or unstated assumption made by the author.
The author falsely equates 'no starvation' with 'no environmental factors.' A severe drought creates two distinct environmental threats: lack of food and lack of water.
To strengthen an argument, you must usually find an option that patches a vulnerability or rules out an alternate explanation.
3
Evaluate the options to find one that bridges the identified gap.
The option regarding freshwater aquifers explicitly eliminates the possibility of dehydration (water scarcity).
Ruling out the most prominent remaining alternative explanation (thirst) forces the conclusion toward the author's preferred explanation (military invasion).

Key Concept

Strengthening causal arguments by eliminating alternative explanations.
Estimated Time:2m 0s
Question 666Question →

Consider the following argument:

Media Scholar: It is widely argued that the mass production of political pamphlets was the primary catalyst for the rapid spread of democratic ideals among the European working class during the 18th century. However, historical records confirm that the literacy rate among this demographic at the time remained firmly below 15 percent. Since the vast majority of these individuals could not read, the diffusion of these revolutionary ideals must have been driven almost entirely by traditional oral communication in public gathering places, functioning completely independent of the printed word.

The media scholar's argument is logically strengthened by newly uncovered historical accounts indicating that 18th-century political pamphlets were regularly read aloud by literate community members to large audiences of illiterate workers in local taverns.

Show answer & explanation

Answer: False

Answer

False
The statement is False because the historical accounts actually weaken the media scholar's argument. The scholar concludes that the spread of ideals functioned 'completely independent of the printed word.' However, the accounts reveal that the oral communication was, in fact, directly reliant on the printed pamphlets. This undermines the scholar's attempt to sever the causal link between the mass production of pamphlets and the spread of democratic ideals.

Step-by-Step Solution

1
Identify the main conclusion of the media scholar's argument.
The conclusion is that the diffusion of democratic ideals was driven by oral communication and functioned completely independent of the printed word.
Understanding the exact scope of the conclusion is necessary to determine what evidence would strengthen or weaken it.
2
Analyze the new evidence provided in the statement.
The evidence states that printed political pamphlets were read aloud to illiterate workers by literate community members.
We must determine how this specific piece of information interacts with the established premises and conclusion.
3
Evaluate the logical impact of the new evidence on the argument.
While the evidence confirms an oral medium was used, it establishes that this oral communication was directly dependent on the printed pamphlets. This contradicts the 'completely independent of the printed word' clause of the conclusion.
Evidence that contradicts a core, explicit component of the conclusion weakens the argument, rather than strengthening it.
4
Determine the truth value of the provided statement.
Since the new evidence weakens the argument, the statement claiming that it strengthens the argument is False.
This directly answers the prompt's evaluation criteria.

Key Concept

Evaluating how new evidence affects an argument by distinguishing between superficial support for a premise and contradiction of a core conclusion.
Estimated Time:1m 30s
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