Examkin

Assumptions in Conditional Logic

15 questions

All types15Multiple choice7True / False4Matching4
Question 1Question →

The city will implement the proposed congestion charge only if the public transit system's capacity is increased by at least 20 percent. Furthermore, the transit system's capacity can be expanded by that amount only if the state legislature approves the pending transit grant. Therefore, unless the state legislature approves the transit grant, the city's downtown air quality will not improve significantly.

The conclusion drawn above depends on which one of the following assumptions?

Show answer & explanation

Answer: The city's downtown air quality will improve significantly only if the proposed congestion charge is implemented.

Answer

The assumption that the city's downtown air quality will improve significantly only if the proposed congestion charge is implemented.
The argument requires a bridge between the failure to implement the congestion charge and the failure of air quality to improve. The premises prove that without the state grant, the congestion charge cannot be implemented. The conclusion states that without the state grant, air quality will not improve. For this to be true, the argument must assume that without the congestion charge, air quality will not improve. This translates logically to 'Air quality improves ONLY IF the congestion charge is implemented.'

Step-by-Step Solution

1
Diagram the conditional premises provided in the argument.
Premise 1: Implement Congestion Charge → Increase Transit Capacity. Premise 2: Increase Transit Capacity → State Grant Approved.
Mapping the explicit conditional statements is the first step in identifying logical gaps.
2
Combine the premises into a logical chain and find its contrapositive.
Chain: Implement Charge → Increase Capacity → State Grant Approved. Contrapositive: NOT State Grant Approved → NOT Increase Capacity → NOT Implement Charge.
Chaining the premises reveals the full scope of what is guaranteed when certain conditions are met or fail to be met.
3
Diagram the conclusion and compare it to the premise chain.
Conclusion: NOT State Grant Approved → NOT Air Quality Improve. We currently only have: NOT State Grant Approved → NOT Implement Charge.
Comparing what we have (premises) to what we need (conclusion) isolates the exact missing link.
4
Identify the missing conditional link (the assumption) that bridges the gap.
To get to 'NOT Air Quality Improve', we must assume: NOT Implement Charge → NOT Air Quality Improve. The contrapositive of this is: Air Quality Improve → Implement Charge (Air quality improves ONLY IF charge is implemented).
A valid argument must connect its premises to its conclusion without logical gaps.

Key Concept

Identifying necessary assumptions in conditional logic chains by diagramming premises, finding their contrapositives, and bridging the gap to the conclusion.
Question 2Question →

Political scientist: A representative democracy is fully insulated from autocratic capture only if its judiciary is strictly impartial and its electorate remains highly informed. However, maintaining a highly informed electorate invariably requires a decentralized media apparatus. Therefore, because any nation that establishes comprehensive algorithmic speech filters inherently dismantles its decentralized media apparatus, it follows that if a representative democracy establishes such filters, its judiciary will inevitably forfeit its strict impartiality.

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

Show answer & explanation

Answer: A representative democracy cannot maintain a strictly impartial judiciary without a highly informed electorate.

Answer

The argument assumes that a representative democracy cannot maintain a strictly impartial judiciary without a highly informed electorate.
The correct answer bridges the precise logical gap in the argument. The premises establish that algorithmic speech filters destroy a decentralized media, which in turn destroys a highly informed electorate. From this proven chain, the author leaps to the conclusion that the judiciary will forfeit its impartiality. This leap is only valid if losing an informed electorate guarantees losing an impartial judiciary (If NOT Informed Electorate -> NOT Impartial Judiciary). The correct answer states this exact relationship: an impartial judiciary cannot be maintained without an informed electorate.

Step-by-Step Solution

1
Map the conditional premises provided in the stimulus.
Insulated -> (Impartial Judiciary AND Informed Electorate). Informed Electorate -> Decentralized Media. Speech Filters -> ~Decentralized Media.
Visualizing the conditional chains reveals the exact boundaries of the stated evidence.
2
Determine the downstream logical effects of the trigger condition found in the conclusion.
The trigger is 'Speech Filters'. Based on the premises: Speech Filters -> ~Decentralized Media -> ~Informed Electorate. Therefore, establishing speech filters guarantees the loss of an informed electorate.
Tracing the conditional chain shows what can be validly inferred directly from the author's evidence.
3
Identify the author's conclusion and isolate the logical gap.
The author concludes: Speech Filters -> ~Impartial Judiciary. However, the premises only prove Speech Filters -> ~Informed Electorate.
To draw this specific conclusion about the judiciary, the author must be relying on an unstated link connecting the loss of an informed electorate to the loss of an impartial judiciary.
4
Formulate the required assumption and apply the Negation Test to confirm.
The required link is ~Informed Electorate -> ~Impartial Judiciary (or equivalently, Impartial Judiciary -> Informed Electorate). Negating this yields: 'A democracy CAN maintain an impartial judiciary even without an informed electorate.' If true, the author's conclusion falls apart.
A necessary assumption must definitively destroy the argument when negated.

Key Concept

Identifying unstated conditional bridges between necessary conditions
Question 3Question →

A municipality is eligible for the Federal Green Grant only if it has successfully reduced its overall carbon emissions for three consecutive years. Oakhaven recently redirected a large portion of its public transit funding to highway expansion, a policy decision that invariably prevents any reduction in local carbon emissions. Therefore, Oakhaven will not be able to revitalize its downtown commercial district.

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

Show answer & explanation

Answer: Revitalizing a downtown commercial district requires a municipality to be eligible for the Federal Green Grant.

Answer

The assumption required by the argument is that revitalizing a downtown commercial district requires a municipality to be eligible for the Federal Green Grant.
The argument establishes that Oakhaven is ineligible for the Federal Green Grant due to its failure to reduce carbon emissions. It then concludes that Oakhaven cannot revitalize its downtown. For this conclusion to logically follow, being ineligible must guarantee the inability to revitalize (Ineligible → Cannot Revitalize). The contrapositive of this conditional relationship is that revitalizing requires eligibility, which is exactly what the correct statement provides.

Step-by-Step Solution

1
Translate the first premise into conditional logic.
Eligible for Grant → Reduced Emissions
To establish the baseline requirements set by the grant policy.
2
Evaluate Oakhaven's actions based on the second premise.
Redirected Funding → Did NOT Reduce Emissions
To determine Oakhaven's factual status regarding the grant requirements.
3
Combine the premises to deduce Oakhaven's grant eligibility.
Because Oakhaven did not reduce emissions, it is NOT eligible for the grant (Modus Tollens).
To find the ultimate logical consequence of Oakhaven's policy decision.
4
Identify the logical gap between the synthesized premise and the conclusion.
Premise fact: Oakhaven is NOT eligible. Conclusion: Oakhaven CANNOT revitalize downtown. The gap is: NOT eligible → CANNOT revitalize.
To pinpoint the exact assumption required to make the argument logically valid.
5
Formulate the contrapositive of the missing link to find the correct answer.
The contrapositive of 'NOT eligible → CANNOT revitalize' is 'Revitalize → Eligible' (Revitalizing requires eligibility).
Because correct answer choices for conditional assumptions frequently appear in their equivalent contrapositive form.

Key Concept

Assumptions in Conditional Logic requires bridging the gap between established premises and the conclusion using strict necessary and sufficient conditions, often relying on the contrapositive of the missing link to formulate the correct answer choice.
Question 4Question →

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

Show answer & explanation

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 5Question →

Unless a species adapts to its changing environment, it will eventually face extinction. The red-eyed tree frog has successfully adapted to its changing environment. Therefore, the red-eyed tree frog will not face extinction.

Is the following statement true or false?
The argument relies on the assumption that adapting to a changing environment is sufficient to prevent a species from facing extinction.

Show answer & explanation

Answer: True

Answer

True
The statement is true. The argument commits a conditional logic error by treating a necessary condition as a sufficient one. The premise states that without adaptation, extinction is guaranteed. The conclusion assumes that with adaptation, survival is guaranteed, meaning the author assumes adaptation is sufficient to prevent extinction.

Step-by-Step Solution

1
Diagram the conditional premise.
Failure to adapt -> Extinction (which means: Avoid Extinction -> Adapt).
To understand the explicit logical constraints of the argument.
2
Diagram the conclusion.
Adapt -> Avoid Extinction.
To isolate the author's final claim.
3
Compare the premise to the conclusion to find the missing link.
The author reverses the premise's logic, treating the necessary condition (adaptation) as a sufficient condition.
To identify the exact assumption required for the argument to make sense.

Key Concept

Identifying missing conditional links and the confusion of necessary and sufficient conditions.
Question 6Question →

Political theorist: A political revolution can be successful only if it has the broad support of the working class. However, a revolution cannot garner broad working-class support unless its leaders clearly articulate a tangible economic benefit to the public. Therefore, the recent uprising in the southern province will definitely not be a successful political revolution.

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

Show answer & explanation

Answer: The leaders of the recent uprising in the southern province failed to clearly articulate a tangible economic benefit to the public.

Answer

The leaders of the recent uprising in the southern province failed to clearly articulate a tangible economic benefit to the public.
The argument relies on a conditional chain: a revolution is successful only if it has broad support, and it has broad support only if leaders articulate an economic benefit (Successful -> Broad Support -> Articulate Benefit). The conclusion asserts that the recent uprising will not be successful. To logically guarantee this conclusion, we must trigger the contrapositive of the chain: if the leaders fail to articulate an economic benefit, the revolution will lack broad support and thus cannot be successful. The correct answer provides this exact missing trigger by stating the leaders failed to articulate the benefit.

Step-by-Step Solution

1
Identify the premises and their conditional relationships.
Premise 1: Successful Revolution -> Broad Working-Class Support. Premise 2: Broad Working-Class Support -> Articulate Economic Benefit.
Mapping the conditional statements is essential for finding the logical structure of the argument.
2
Combine the premises to form a logical chain.
Successful Revolution -> Broad Working-Class Support -> Articulate Economic Benefit.
Chaining the premises reveals the ultimate necessary conditions for a successful revolution.
3
Determine the contrapositive of the logical chain.
If leaders DO NOT articulate an economic benefit -> NO broad support -> NOT a successful revolution.
The conclusion asserts a negative outcome (the uprising will not be successful), so the contrapositive shows what triggers that specific outcome.
4
Identify the missing link required to logically guarantee the conclusion.
The argument concludes the recent uprising will NOT be successful. To prove this using the contrapositive chain, we must assume that the uprising's leaders failed to articulate a tangible economic benefit.
Adding this assumption triggers the contrapositive chain, which definitively proves the conclusion.

Key Concept

Sufficient Assumptions and Contrapositives in Conditional Logic
Estimated Time:1m 30s
Question 7Question →

Whenever a restaurant fails to maintain strict hygiene standards, it receives negative reviews from local food critics. The new seafood diner in town has consistently failed to maintain strict hygiene standards. Therefore, the new seafood diner will be forced to close down within the year.

The conclusion drawn above follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Any restaurant that receives negative reviews from local food critics will be forced to close down within the year.

Answer

Any restaurant that receives negative reviews from local food critics will be forced to close down within the year.
The argument establishes that the diner will receive negative reviews, but then concludes it will be forced to close down. For this conclusion to logically follow, there must be a strict rule guaranteeing that receiving negative reviews leads to closing down. The correct option provides this exact necessary bridge, acting as a sufficient assumption.

Step-by-Step Solution

1
Identify the premises and the main conclusion of the argument.
Premise 1: Fails hygiene standards -> Negative reviews. Premise 2: Seafood diner -> Fails hygiene standards. Conclusion: Seafood diner -> Forced to close down.
Breaking down the argument into formal conditional logic helps isolate the missing link.
2
Determine the intermediate conclusion established by the premises.
Since the seafood diner fails hygiene standards, it will receive negative reviews (Seafood diner -> Negative reviews).
This connects the specific subject of the argument to the established conditional rule.
3
Identify the logical gap between the intermediate conclusion and the main conclusion.
The argument leaps from the fact that the diner will receive negative reviews to the claim that it will be forced to close down.
To make the conclusion follow logically, we need a conditional rule connecting 'negative reviews' to 'forced to close down'.
4
Formulate the necessary assumption to bridge this gap.
The correct assumption must state: If a restaurant receives negative reviews, it will be forced to close down (Negative reviews -> Forced to close down).
This completes the logical chain (A -> B, B -> C), guaranteeing the conclusion is true.

Key Concept

Bridging gaps in conditional logic chains to justify a conclusion.
Estimated Time:1m 0s
Question 8Question →

The following arguments each rely on an unstated conditional premise to bridge their evidence to their conclusion. Match each argument with the strictly necessary conditional assumption that logically completes its reasoning.

Click a left item, then click its matching right item

Items

The rare alpine orchids require soil with a highly specific mineral composition to survive in the biodome. Since the researchers have successfully synthesized soil that perfectly mimics this composition, it is guaranteed that the orchids will survive.
The city council refuses to raise commercial property taxes this fiscal year. Therefore, the new urban zoning initiative will fail to reduce downtown traffic congestion.
A corporation is subject to federal antitrust scrutiny only when its domestic market share exceeds forty percent. Apex Industries recently acquired its largest competitor, bringing its market share to forty-five percent. Consequently, Apex Industries will now face federal antitrust scrutiny.
An action can be considered morally praiseworthy only if it is performed entirely out of a sense of duty. The altruistic actions performed by our local volunteers are motivated by deep empathy for others. Therefore, the actions of these volunteers are not morally praiseworthy.

Matches

Show answer & explanation

Answer

Match the orchid argument with the assumption making synthesized soil sufficient for survival; match the traffic argument with the assumption making tax raises necessary for reducing congestion; match the antitrust argument with the assumption making market share sufficient for scrutiny; match the altruism argument with the assumption making empathy mutually exclusive with duty.
Each correct pairing provides the exact formal logical bridge required to make the conclusion of the corresponding argument valid, repairing illegal reversals, linking disparate terms, and forming logically sound contrapositives.

Step-by-Step Solution

1
Analyze the alpine orchids argument.
Identified the argument treats a necessary condition (mineral soil) as sufficient. Matches with the premise establishing that providing the soil guarantees survival.
To prove the conclusion that the orchids will survive, the necessary condition must be formally elevated to a sufficient condition.
2
Analyze the traffic congestion argument.
Identified a missing link between not raising taxes and not reducing congestion. Matches with the premise stating congestion cannot be reduced unless taxes are raised.
The conclusion relies on the contrapositive of the missing premise: If congestion is reduced, taxes are raised. Since taxes are not raised, congestion is not reduced.
3
Analyze the antitrust scrutiny argument.
Identified an illegal reversal involving 'only when'. Matches with the premise stating every corporation with over forty percent market share faces scrutiny.
The argument provides the necessary condition (forty-five percent share) but illicitly concludes the result. The assumption must dictate that the condition is sufficient to guarantee the result.
4
Analyze the moral praiseworthiness argument.
Identified two unconnected sufficient terms (empathy and duty). Matches with the premise stating empathy and duty are mutually exclusive.
To conclude an action is not praiseworthy because it lacks duty (since it was driven by empathy), the author must assume that having empathy means the action was not done entirely out of duty.

Key Concept

Identifying unstated conditional premises and recognizing illegal reversals (confusing necessary and sufficient conditions) in logical arguments.
Question 9Question →

Read the following argument:

Any regulatory policy that restricts individual liberties is justified only if it prevents a significant public harm. The newly proposed zoning ordinance will undeniably restrict property owners' liberties. However, this ordinance was designed strictly to increase local tax revenues rather than to address any significant public harm. Therefore, the newly proposed zoning ordinance is not justified.

Statement: The argument's conclusion follows logically if it is assumed that a regulatory policy cannot prevent a significant public harm unless it was explicitly designed to address one.

Show answer & explanation

Answer: True

Answer

True
The statement is true because it provides the exact conditional contrapositive needed to bridge the argument's conceptual gap. It connects the premise (the policy lacks the intent to address harm) to the rule's necessary condition (the policy fails to actually prevent harm), thereby guaranteeing the conclusion.

Step-by-Step Solution

1
Deconstruct the conditional rule established in the first sentence.
Rule: If a policy restricts liberties (RL), then (Justified (J) → Prevents Significant Public Harm (PSPH)). Contrapositive: If RL, and NOT PSPH → NOT J.
Identifying the formal logic relationships dictated by 'only if' is mandatory to evaluate the structural validity of the conclusion.
2
Analyze the premises provided specifically about the zoning ordinance.
Premise A: The ordinance restricts liberties (RL). Premise B: The ordinance is NOT designed to address a significant public harm (NOT DPSPH).
We must isolate the exact evidence the author relies upon to attempt to trigger the conclusion.
3
Identify the conclusion and pinpoint the logical gap.
Conclusion: The ordinance is NOT justified (NOT J). The gap exists between the premise 'NOT designed to address harm' (intent) and the required trigger 'does NOT prevent harm' (effect).
To prove NOT J using the rule from Step 1, the argument must prove NOT PSPH. The author improperly assumes NOT DPSPH is sufficient to prove NOT PSPH.
4
Translate the proposed statement and evaluate its logical impact on the argument.
Statement: 'Cannot prevent harm (PSPH) unless designed to do so (DPSPH)' translates to PSPH → DPSPH. The contrapositive is NOT DPSPH → NOT PSPH. Applying this to our premise yields NOT PSPH, which definitively proves NOT J.
We must test if the statement functions as a mathematically sound sufficient assumption that completely seals the logical gap.

Key Concept

Bridging Intent and Effect through Sufficient Assumptions (Only If / Unless)
Question 10Question →

The survival of the coral reef ecosystem in the Sapphire Atoll requires a continuous presence of parrotfish. Parrotfish, however, can maintain their populations only if there is a low concentration of acidic pollutants in the surrounding water. It has been recently established that heavy industrial runoff from the mainland introduces high levels of heavy metals into the atoll. Therefore, whenever the atoll experiences heavy industrial runoff, the coral reef ecosystem will ultimately fail to survive.

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

Show answer & explanation

Answer: The introduction of high levels of heavy metals into the atoll precludes a low concentration of acidic pollutants in the water.

Answer

The statement asserting that the introduction of high levels of heavy metals into the atoll precludes a low concentration of acidic pollutants in the water.
The argument depends on linking the new information introduced in the premises (heavy metals) to the causal chain that leads to the destruction of the reef. The premises establish that survival requires parrotfish, and parrotfish require low acid. Thus, a lack of low acid guarantees the reef will not survive. The argument concludes that heavy runoff guarantees the reef will not survive, based strictly on the fact that runoff introduces heavy metals. For this to make sense, the heavy metals must cause the lack of low acid. By stating that heavy metals preclude low acid, this option perfectly bridges the gap in the conditional chain.

Step-by-Step Solution

1
Analyze the conditional statements in the premises.
Survival requires Parrotfish (Survival -> Parrotfish). Parrotfish require Low Acid (Parrotfish -> Low Acid). Heavy Runoff introduces Heavy Metals (Runoff -> Heavy Metals).
Identifying the formal logic structure is the first step in finding the missing structural link.
2
Analyze the conditional statement in the conclusion.
Heavy Runoff guarantees a failure to survive (Runoff -> NOT Survival).
Understanding the final claim determines what the premises must logically prove to make the argument valid.
3
Chain the premises and find the logical gap.
The conclusion requires linking Runoff to NOT Survival. We know Runoff -> Heavy Metals. By contrapositive, NOT Low Acid -> NOT Parrotfish -> NOT Survival. To connect these halves (Runoff -> Heavy Metals ... NOT Low Acid -> NOT Survival), we need a bridge between Heavy Metals and NOT Low Acid.
An argument relying on a conditional chain is only valid if all terms leading from the sufficient condition to the necessary condition are properly connected.
4
Formulate the required assumption and apply the Negation Test.
The required assumption is that Heavy Metals -> NOT Low Acid (Heavy metals preclude low acid). If negated, heavy metals would NOT prevent low acid, which means runoff could occur without disrupting the conditions necessary for survival, destroying the conclusion.
A necessary assumption must be required for the conclusion to stand; if its negation invalidates the argument, it is the correct answer.

Key Concept

Assumptions in Conditional Logic
Estimated Time:2m 0s
Question 11Question →

Analyze the four conditional arguments below. Match each argument (left) with the specific missing assumption (right) that is logically sufficient to bridge the gap between the argument's premises and its conclusion.

Click a left item, then click its matching right item

Items

A municipality is eligible for the state urban renewal grant only if its population density exceeds 5,000 residents per square mile. The municipality of Springfield recently constructed three expansive suburban housing developments. Therefore, Springfield is not eligible for the state urban renewal grant.
Unless a pharmaceutical company completes a comprehensive Phase III clinical trial, its novel therapeutic drug will not be approved by the federal regulatory board. Apex Pharma's novel cardiovascular drug was officially approved by the board today. Thus, Apex Pharma's drug must have been tested on a genetically diverse patient population.
Any biomedical research project that utilizes CRISPR-edited embryonic stem cells requires rigorous federal oversight to proceed legally. Dr. Aris's current neurological research project does not require rigorous federal oversight to proceed legally. Therefore, Dr. Aris's current project is not funded by the National Science Institute.
If an autonomous vehicle's navigation system relies exclusively on optical cameras, it will fail to operate safely in severely inclement weather. The newly released Zenith self-driving car operates perfectly safely in severely inclement weather. Therefore, the Zenith car must incorporate active lidar sensor technology.

Matches

Show answer & explanation

Answer

Argument 1 pairs with Assumption 1, Argument 2 with Assumption 2, Argument 3 with Assumption 3, and Argument 4 with Assumption 4.
Each argument contains a stranded premise and a conclusion that requires a specific conditional link to be logically valid. By applying the contrapositive and properly diagramming the conditional indicators ('unless', 'only if', 'any', 'if'), the exact missing sufficient assumption can be identified and mapped to each argument.

Step-by-Step Solution

1
Translate the conditional rules in each argument's premises into formal logic.
Arg 1: Eligible -> >5000. Arg 2: Approved -> Phase III. Arg 3: CRISPR -> Oversight. Arg 4: Exclusively Optical -> Fail Safely.
Accurately diagramming conditional indicators ('only if', 'unless', 'any', 'if') is required to identify the logical endpoints of the existing premises.
2
Determine the intermediate inference drawn from the application of the second premise.
Arg 1: No direct inference yet. Arg 2: Apex completed Phase III. Arg 3: Dr. Aris does not use CRISPR. Arg 4: Zenith is not Exclusively Optical.
The intermediate inference reveals what the argument has successfully proven before jumping to its unsupported conclusion.
3
Identify the logical gap between the intermediate inference and the stated conclusion.
Arg 1 needs: Constructed Housing -> Density ≤ 5000. Arg 2 needs: Phase III -> Diverse. Arg 3 needs: Not CRISPR -> Not NSI Funded (or NSI -> CRISPR). Arg 4 needs: Not Exclusively Optical -> Lidar.
A sufficient assumption must perfectly connect the proven inference to the unproven conclusion without triggering logical fallacies.
4
Evaluate the right-side items to find the exact conditional matches.
The assumptions provided directly reflect the exact gaps identified in Step 3.
Matching the derived necessary/sufficient bridges confirms the correct pairings.

Key Concept

Assumptions in Conditional Logic
Estimated Time:3m 0s
Question 12Question →

Read the following argument and evaluate the statement below it.

Argument: A pharmaceutical company can receive expedited regulatory approval for a new drug only if the drug treats a life-threatening condition and demonstrates significant clinical improvement over existing therapies. Vaxica's new drug demonstrates significant clinical improvement over existing therapies, yet the regulatory board denied it expedited approval. Therefore, Vaxica's new drug must not treat a life-threatening condition.

Statement: The argument's reasoning relies on assuming that treating a life-threatening condition and demonstrating significant clinical improvement over existing therapies are sufficient conditions for receiving expedited regulatory approval.

Show answer & explanation

Answer: True

Answer

True
The statement is true because the argument commits a classic formal logic flaw: confusing necessary and sufficient conditions. The phrase 'only if' indicates that treating a life-threatening condition and demonstrating improvement are necessary for approval. By concluding that the drug must lack the first condition simply because it was denied approval (despite meeting the second condition), the author assumes that there are no other possible reasons for denial. This is logically identical to assuming that meeting those two conditions is sufficient to guarantee approval.

Step-by-Step Solution

1
Diagram the conditional logic in the argument's premises.
Premise 1: Expedited Approval → Treats Life-Threatening Condition (L) AND Demonstrates Improvement (I). Premise 2: Drug has I. Premise 3: Drug does NOT have Expedited Approval.
Mapping the explicit conditional statements is necessary to identify logical gaps.
2
Analyze the argument's conclusion in relation to the premises.
The conclusion is that the drug does NOT have L. The author infers the absence of one necessary condition from the absence of the sufficient condition.
Understanding how the author attempts to connect the evidence to the conclusion reveals the unstated assumption.
3
Apply the Negation Test to the proposed assumption.
Negated assumption: L and I are NOT sufficient for Expedited Approval. If true, the drug could have L and I, but still be denied approval. In this scenario, knowing the drug was denied approval and has I does NOT prove it lacks L.
The Negation Test definitively proves whether an assumption is strictly necessary for an argument's conclusion to follow.
4
Evaluate the statement based on the Negation Test.
Because negating the assumption destroys the argument, the assumption is logically required. Therefore, the statement is True.
An argument relies on an assumption if the argument fails when that assumption is false.

Key Concept

Necessary vs. Sufficient Conditions and the Negation Test
Estimated Time:1m 30s
Question 13Question →

Consider the argument below regarding historical artifacts:

A historical artifact is considered authentic only if its provenance can be verified through continuous independent documentation. The recently discovered chalice lacks any continuous independent documentation of its provenance. Therefore, the chalice cannot be considered an authentic historical artifact.

The argument above logically depends on the assumption that any historical artifact whose provenance can be verified through continuous independent documentation is considered authentic.

Show answer & explanation

Answer: False

Answer

False
The statement is false because the provided argument is already logically valid and complete. It correctly uses the contrapositive of its stated premise (Authentic -> Provenance Verified) to safely reach the conclusion (~Provenance Verified -> ~Authentic). It does not require or rely on the reversed assumption that verifiable provenance guarantees authenticity.

Step-by-Step Solution

1
Translate the argument's first sentence into a formal conditional relationship.
The phrase 'only if' introduces a necessary condition. The relationship is: Authentic -> Provenance Verified.
Identifying the exact conditional relationship is required to evaluate the logical structure of the argument.
2
Analyze the second premise and the conclusion.
The argument states that the chalice does not have verified provenance (~Provenance Verified), and concludes it is not authentic (~Authentic).
This maps the specific scenario to the established conditional rule.
3
Evaluate the validity of the argument's deduction.
The argument correctly applies the contrapositive principle (~Provenance Verified -> ~Authentic). The reasoning is completely sound without any missing links.
A logically sound argument relies only on its stated premises and valid rules of inference; it does not require any additional unstated assumptions.
4
Analyze the assumption provided in the statement.
The statement claims the argument relies on the assumption 'Provenance Verified -> Authentic'. Because the argument is already valid, it does not rely on this reversed condition.
This confirms that the provided statement incorrectly evaluates the logical dependencies of the argument.

Key Concept

Evaluating whether a conditional argument requires an additional assumption, and distinguishing between valid deductions (contrapositive) and invalid assumptions (illegal reversal).
Question 14Question →

Chief Engineer: A spacecraft's life-support system can sustain a crew during a deep-space voyage only if it features a regenerative carbon dioxide scrubber. Therefore, any spacecraft commissioned for the Outer Planets Initiative must feature a regenerative carbon dioxide scrubber.

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

Show answer & explanation

Answer: Every spacecraft commissioned for the Outer Planets Initiative requires a life-support system that can sustain a crew during a deep-space voyage.

Answer

Every spacecraft commissioned for the Outer Planets Initiative requires a life-support system that can sustain a crew during a deep-space voyage.
The argument relies on conditional reasoning. The premise establishes that sustaining a crew in deep space requires a regenerative scrubber. The conclusion claims that spacecraft in the Outer Planets Initiative must have this scrubber. To logically connect the premise to the conclusion, the argument must assume that spacecraft in the Initiative are required to sustain a crew in deep space. Without this bridge, the premise about sustaining a crew would be entirely irrelevant to the Initiative's spacecraft.

Step-by-Step Solution

1
Identify the core conditional premise provided in the argument.
Sustain a crew in deep space -> Features a regenerative scrubber.
The phrase 'only if' introduces a necessary condition that must be met.
2
Identify the main conclusion drawn by the chief engineer.
Outer Planets Initiative spacecraft -> Features a regenerative scrubber.
The transition word 'Therefore' indicates the final claim the author is trying to prove.
3
Identify the logical gap between the premise and the conclusion.
The argument jumps from a requirement for sustaining a crew to a requirement for Outer Planets Initiative spacecraft.
To prove that the Initiative spacecraft need scrubbers, there must be a connecting link showing that these specific spacecraft are required to sustain a crew.
4
Formulate the necessary assumption and verify it using the Negation Test.
Assumption: Outer Planets Initiative spacecraft -> Sustain a crew. Negation: Some Initiative spacecraft do not need to sustain a crew. If the negation is true, the conclusion fails because those spacecraft wouldn't strictly need the scrubber.
The Negation Test confirms that this conditional bridge is an absolute logical requirement for the argument to hold.

Key Concept

Identifying necessary assumptions to bridge structural gaps in conditional reasoning chains.
Estimated Time:1m 30s
Question 15Question →

Analyze the following arguments, each of which relies on an unstated assumption involving conditional logic. Match each argument to the necessary or sufficient assumption that logically bridges the gap between its premises and its conclusion.

Click a left item, then click its matching right item

Items

The metropolitan area will drastically reduce its carbon footprint if commuters adopt mass transit en masse. The city council's newly approved subsidy plan aggressively targets suburban train ticket prices. Therefore, the metropolitan area will drastically reduce its carbon footprint.
A geological fault line is highly active only if it registers micro-tremors on a weekly basis. The Cascade fault system is known to be highly active. Therefore, the Cascade fault system must have recently exhibited significant geothermal venting.
The university's endowment will grow significantly this year. After all, the endowment grows significantly whenever alumni donations increase, and the university recently launched a highly praised career networking platform.
A renewable energy grid cannot be considered stable unless it includes massive battery storage facilities. Therefore, the coastal wind farm project's new grid will not be considered stable, because it relies heavily on short-term federal grants.

Matches

Show answer & explanation

Answer

Argument 1 matches with the commuter subsidy bridge; Argument 2 matches with the contrapositive linking venting to tremors; Argument 3 matches with the platform-to-donations guarantee; and Argument 4 matches with the federal grants to battery storage connection.
Each correct pair seamlessly connects the factual premise of the argument to the conditional trigger required to validate the conclusion. When necessary, the assumption is presented in its logically equivalent contrapositive form (as seen in the geology argument).

Step-by-Step Solution

1
Map the formal logic of each argument's premises and conclusion.
Identify the conditional triggers: 'if' (sufficient), 'only if' (necessary), 'whenever' (sufficient), and 'unless' (necessary).
Accurately diagramming the stated conditions is required before the missing link can be identified.
2
Identify the 'dangling' terms in the premises and conclusion to find the logical gap.
For example, in the geological argument, the premises arrive at 'registers micro-tremors', but the conclusion introduces 'geothermal venting'.
The correct assumption must perfectly bridge these unmatched terms without introducing outside information.
3
Evaluate the assumption choices for direct conditional links or logically equivalent contrapositives.
The geological gap (Micro-tremors -> Geothermal Venting) is satisfied by finding its contrapositive (No Venting -> No Micro-tremors) in the available choices.
Test makers frequently hide the correct bridging assumption by stating it in its contrapositive form.

Key Concept

Bridging logical gaps using sufficient/necessary assumptions and recognizing their contrapositives.