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Parallel Conditional Logic

18 questions

All types18Multiple choice9True / False5Matching4
Question 1Question →

Analyze the natural language arguments below. Match each argument to its corresponding formal symbolic conditional skeleton.

Click a left item, then click its matching right item

Items

If a species is considered invasive, it threatens local biodiversity. Any species that threatens local biodiversity is subject to removal. Therefore, if a species is considered invasive, it is subject to removal.
An applicant will be approved for the advanced grant only if they have published peer-reviewed research. Dr. Aris has not published peer-reviewed research. Consequently, Dr. Aris will not be approved for the advanced grant.
A robust marketing campaign is required for a startup to achieve profitability. The startup TechNova recently launched a robust marketing campaign. It follows that TechNova will achieve profitability.
Provided that a contract includes a non-compete clause, it is legally binding. The new employment contract does not include a non-compete clause. Thus, the new employment contract is not legally binding.

Matches

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Answer

Argument 1 matches the Valid Chain; Argument 2 matches the Valid Contrapositive; Argument 3 matches the Flawed Reversal; Argument 4 matches the Flawed Negation.
Each argument translates to a specific symbolic structure based on its conditional indicators. By identifying whether a condition is sufficient ('if', 'any', 'provided that') or necessary ('only if', 'is required for'), we can diagram the argument properly and classify it as a valid deduction or a formal flaw.

Step-by-Step Solution

1
Diagram Argument 1.
Invasive (X) → Threatens (Y); Threatens (Y) → Removal (Z). Conclusion: Invasive (X) → Removal (Z).
The indicators 'If' and 'Any' both introduce sufficient conditions, creating a Valid Transitive Chain.
2
Diagram Argument 2.
Approved (X) → Published (Y); ~Published (~Y). Conclusion: ~Approved (~X).
The indicator 'only if' introduces a necessary condition. Denying it yields a Valid Contrapositive.
3
Diagram Argument 3.
Profitability (X) → Marketing (Y); Marketing (Y). Conclusion: Profitability (X).
The phrase 'is required for' introduces a necessary condition. Affirming it to prove the sufficient condition is a Flawed Reversal.
4
Diagram Argument 4.
Non-compete (X) → Binding (Y); ~Non-compete (~X). Conclusion: ~Binding (~Y).
The phrase 'Provided that' introduces a sufficient condition. Denying it to disprove the necessary condition is a Flawed Negation.

Key Concept

Identifying formal conditional logic structures (valid deductions vs. formal flaws) in natural language arguments.
Question 2Question →

According to the city's new preservation guidelines, if a building is to be designated as a historical landmark, it must preserve its original exterior facade and be structurally reinforced against earthquakes. Furthermore, if a building is constructed of unreinforced masonry, it cannot be structurally reinforced against earthquakes. The old municipal library is constructed of unreinforced masonry. Therefore, the old municipal library will not be designated as a historical landmark.

Which of the following arguments exhibits a pattern of reasoning most logically parallel to that demonstrated in the argument above?

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Answer: According to the hospital's protocol, if a patient is to be prescribed the experimental medication, they must possess normal kidney function and be closely monitored by a specialist. If a patient resides in a rural area, they cannot be closely monitored by a specialist. Patient Jones resides in a rural area. Therefore, Patient Jones will not be prescribed the experimental medication.

Answer

The argument concerning Patient Jones being denied the experimental medication due to residing in a rural area.
The stimulus argument employs a valid form of conditional reasoning using a conditional chain to trigger the contrapositive of a compound necessary condition. It states that two conditions are necessary for a building to become a landmark (A → B and C). It then introduces a second conditional rule establishing that a certain characteristic prevents one of those necessary conditions (D → ~C), and applies this to a specific case (X is D) to validly conclude the sufficient condition cannot occur (X is ~A). The correct answer perfectly mirrors this structure: it establishes two necessary conditions for a medication prescription, introduces a second rule showing a characteristic prevents one of those conditions, and validly concludes the medication will not be prescribed for a patient with that characteristic.

Step-by-Step Solution

1
Analyze the logical structure of the primary conditional premise in the stimulus.
The stimulus establishes a conditional rule with a compound necessary condition: Landmark → (Preserve Facade AND Structural Reinforcement).
Identifying the formal symbolic structure of the primary rule is required to find an exact structural match.
2
Determine the deduction pattern used to reach the conclusion in the stimulus.
The argument introduces a secondary rule (Unreinforced Masonry → ~Structural Reinforcement) and applies it to a specific case (Library is Unreinforced Masonry) to prove one necessary condition is not met. It then validly concludes the sufficient condition cannot occur (~Landmark).
Parallel reasoning requires matching the specific conditional chain and the valid reasoning pattern leading to the conclusion.
3
Evaluate the answer choices to find the identical logical skeleton.
The correct choice must feature: A → (B AND C); D → ~C; X is D; therefore, X is ~A.
Eliminating choices with structural mismatches (single condition, 'or' instead of 'and') or logical flaws (illegal reversal/negation) is necessary to isolate the perfect match.
4
Identify the matching option.
The hospital protocol argument matches exactly: Prescribed → (Kidney Function AND Monitored); Rural → ~Monitored; Jones is Rural; therefore, Jones is ~Prescribed.
This option shares the exact validity, conditional complexity, and chain structure of the stimulus argument.

Key Concept

Parallel Conditional Logic
Question 3Question →

Any soil treatment designed to maximize crop yield must contain high levels of nitrogen. However, no organic fertilizer contains high levels of nitrogen. Therefore, no organic fertilizer is designed to maximize crop yield.

Which one of the following arguments is most similar in its logical features to the argument above?

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Answer: Every properly drafted legal contract includes a severability clause. No document written by a layperson includes a severability clause. Hence, no document written by a layperson is a properly drafted legal contract.

Answer

The argument demonstrating that since every properly drafted legal contract includes a severability clause, and no document written by a layperson includes one, no document written by a layperson is properly drafted.
The correct answer perfectly replicates the formal logical structure of the stimulus. The stimulus argues: All A are B (Yield -> Nitrogen); No C is B (Organic -> ~Nitrogen); Therefore, no C is A (Organic -> ~Yield). The correct option identically reasons: All A are B (Properly drafted -> Severability); No C is B (Layperson -> ~Severability); Therefore, no C is A (Layperson -> ~Properly drafted). Both are valid applications of contrapositive reasoning using matching absolute quantifiers.

Step-by-Step Solution

1
Abstract the formal logic of the stimulus.
Premise 1: Maximize Yield (M) -> High Nitrogen (H). Premise 2: Organic (O) -> ~High Nitrogen (~H). Conclusion: Organic (O) -> ~Maximize Yield (~M).
Identifying the symbolic structure reveals a valid application of the contrapositive across a universal 'no' statement.
2
Summarize the argument's core pattern.
The pattern is: All A are B; No C is B; Therefore, No C is A.
This abstracted template serves as the blueprint for evaluating the answer choices.
3
Evaluate the answer choices against the established blueprint.
Only the option discussing legal contracts matches the template: Properly Drafted (A) -> Severability (B); Layperson (C) -> ~Severability (~B); Therefore, Layperson (C) -> ~Properly Drafted (~A).
Finding an exact structural match, including validity and quantifier strength, is required to correctly answer a parallel reasoning question.

Key Concept

Parallel Conditional Logic
Question 4Question →

If an architectural firm is to win the city's waterfront redevelopment contract, it must either incorporate extensive green spaces into its design or partner with a prominent local engineering company. However, a firm cannot partner with a prominent local engineering company unless it agrees to a profit-sharing model dictated by the city council. The Apex Architectural Group steadfastly refuses to agree to any profit-sharing model. Thus, if Apex is to win the waterfront redevelopment contract, it must incorporate extensive green spaces into its design.

Which one of the following arguments exhibits a pattern of reasoning most logically similar to that exhibited by the argument above?

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Answer: If a new drug is to be approved for treating the rare disease, it must either demonstrate unprecedented efficacy or have no severe side effects. A drug can have no severe side effects only if its active compound is synthesized at low temperatures. The experimental drug X-12 cannot be synthesized at low temperatures. Therefore, if X-12 is to be approved for treating the rare disease, it must demonstrate unprecedented efficacy.

Answer

The argument concerning the new drug approval perfectly parallels the logical structure of the architectural firm stimulus.
The correct answer perfectly mirrors the logical skeleton of the stimulus. Both arguments state a sufficient condition that requires at least one of two necessary conditions. They then establish a further necessary condition for one of the original disjuncts, demonstrate that a specific subject fails to meet this further condition, and validly conclude that if the subject fulfills the initial sufficient condition, it must satisfy the remaining necessary condition.

Step-by-Step Solution

1
Translate the stimulus into formal logic.
Win Contract (W) -> Green Spaces (G) OR Partner (P). Partner (P) -> Profit Sharing (S) (from 'cannot P unless S'). Apex: ~S. Therefore, Apex: ~P. Conclusion: For Apex, W -> G.
Identifying the precise conditional relationships and the valid chain of deductions is required to find an exact structural parallel.
2
Analyze the correct option's logical structure.
Approved (A) -> Efficacy (E) OR No Side Effects (N). No Side Effects (N) -> Low Temp (L) (from 'N only if L'). Drug X-12: ~L. Therefore, X-12: ~N. Conclusion: For X-12, A -> E.
Mapping the candidate argument demonstrates 1:1 structural isomorphism with the stimulus.
3
Evaluate the distractors for structural deviations.
The software argument concludes B -> A (illegal reversal). The novel argument concludes ~A -> ~B (illegal negation). The mayoral argument reaches an absolute rather than conditional conclusion. The athlete argument commits a necessary/sufficient flaw by affirming the consequent in the secondary premise.
Parallel reasoning requires exact logical equivalence; any formal flaw or mismatch in conclusion modality eliminates the option.

Key Concept

Parallel Conditional Logic
Question 5Question →

If the city council approves the new zoning laws, the construction of the shopping mall will begin. If the construction of the shopping mall begins, the local traffic will increase significantly. Therefore, if the city council approves the new zoning laws, the local traffic will increase significantly.

Which one of the following arguments exhibits a pattern of reasoning most similar to that exhibited by the argument above?

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Answer: If the chef uses fresh herbs, the dish will be flavorful. If the dish is flavorful, the customers will be satisfied. Therefore, if the chef uses fresh herbs, the customers will be satisfied.

Answer

The argument about the chef using fresh herbs to satisfy customers.
The correct answer exactly mirrors the valid conditional chain presented in the stimulus. It sets up two conditional premises where the necessary condition of the first becomes the sufficient condition of the second (If A then B; If B then C), and validly concludes that the first sufficient condition guarantees the final necessary condition (If A then C).

Step-by-Step Solution

1
Analyze the logical structure of the stimulus.
The stimulus follows the valid transitive property: Premise 1 (If A -> B), Premise 2 (If B -> C), Conclusion (Therefore, if A -> C).
Identifying the formal structure of the original argument is required to find its exact structural match.
2
Evaluate the structure of the answer choices to find an identical match.
The correct answer has the exact same structure: Premise 1 (If Herbs -> Flavor), Premise 2 (If Flavor -> Satisfaction), Conclusion (Therefore, if Herbs -> Satisfaction).
A parallel reasoning question requires finding the option with the same exact logical validity and premise-conclusion relationship.

Key Concept

Parallel Conditional Logic
Question 6Question →

Consider the following two arguments:

Argument 1: If the orchestra performs a symphony, the concert will last over two hours. The orchestra is performing a symphony tonight. Thus, the concert will last over two hours.

Argument 2: If the temperature drops below freezing, the fountain will be turned off. The fountain is turned off tonight. Thus, the temperature dropped below freezing.

The pattern of reasoning in Argument 2 is logically parallel to the pattern of reasoning in Argument 1.

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Answer: False

Answer

False
The statement is False because the two arguments use different structural deductions. Argument 1 uses a valid logical structure (If A then B; A is true; therefore B is true). Argument 2 uses an invalid logical flaw known as affirming the consequent (If A then B; B is true; therefore A is true). Because their logical structures do not match, the reasoning is not parallel.

Step-by-Step Solution

1
Analyze the logical structure of Argument 1.
Argument 1 structure: If A (performs symphony) -> B (lasts over two hours). A is true. Therefore, B is true. This is a valid deduction.
Identifying the baseline structure is necessary to have a point of comparison.
2
Analyze the logical structure of Argument 2.
Argument 2 structure: If C (temperature drops) -> D (fountain turned off). D is true. Therefore, C is true. This is an invalid deduction (affirming the consequent).
Identifying the second structure allows for structural comparison with the first argument.
3
Compare the two logical structures to determine if they are parallel.
Argument 1 is a valid Modus Ponens structure, while Argument 2 is a flawed structure that affirms the consequent. They are not parallel.
Parallel reasoning requires the arguments to share the exact same logical framework, including validity.

Key Concept

Parallel Conditional Logic
Question 7Question →

Match each natural language argument below to its exact underlying formal symbolic structure. Use the variables XX, YY, and ZZ to represent the distinct propositions in the order they logically arise in the text.

Click a left item, then click its matching right item

Items

Failure to ratify the treaty by the deadline guarantees that economic sanctions will be imposed. However, economic sanctions are imposed against a nation only if it possesses significant natural resources. Consequently, any nation lacking significant natural resources must have ratified the treaty by the deadline.
Unless a corporation undergoes rigorous internal auditing, its stock valuation will not stabilize. Yet, a corporation's stock valuation stabilizes only if investor confidence remains high. Therefore, if a corporation undergoes rigorous internal auditing, its investor confidence will remain high.
A scientific theory achieves mainstream acceptance only if it flawlessly explains existing empirical anomalies. Furthermore, to flawlessly explain existing empirical anomalies, a theory must introduce novel mathematical frameworks. Thus, any theory that does not introduce novel mathematical frameworks cannot achieve mainstream acceptance.
No comprehensive infrastructure plan is considered viable if it relies on unchecked foreign debt. Moreover, any initiative that relies on unchecked foreign debt is universally opposed by the conservative coalition. Hence, all comprehensive infrastructure plans considered viable are supported by the conservative coalition.

Matches

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Answer

The arguments map to the symbolic structures by isolating conditional indicators. The treaty argument translates to the valid negated chain. The auditing argument matches the flawed chain. The scientific theory argument matches the valid transitive chain. The infrastructure argument matches the flawed sufficient deduction.
Matching each natural language argument to its symbolic skeleton requires isolating the conditional indicators ('unless', 'only if', 'guarantees', 'no X if Y') and mapping them accurately to antecedents and consequents. The treaty and theory arguments employ valid reasoning frameworks (contrapositives and transitive chains). The auditing argument commits an illegal reversal flaw, and the infrastructure argument improperly links two outcomes of a shared sufficient condition.

Step-by-Step Solution

1
Translate the treaty argument into formal logic.
The argument becomes ∼X→Y\sim X \rightarrow Y and Y→ZY \rightarrow Z, concluding ∼Z→X\sim Z \rightarrow X.
This establishes the exact structural skeleton for the first stimulus, recognizing 'guarantees' as a sufficient indicator and 'only if' as a necessary indicator.
2
Translate the auditing argument into formal logic.
The argument becomes ∼X→∼Y\sim X \rightarrow \sim Y and Y→ZY \rightarrow Z, concluding X→ZX \rightarrow Z.
This isolates the flawed conditional logic by correctly mapping 'unless' as 'if not'.
3
Translate the scientific theory argument into formal logic.
The argument becomes X→YX \rightarrow Y and Y→ZY \rightarrow Z, concluding ∼Z→∼X\sim Z \rightarrow \sim X.
This isolates the valid transitive reasoning and contrapositive application in the third stimulus.
4
Translate the infrastructure argument into formal logic.
The argument becomes X→∼YX \rightarrow \sim Y and X→ZX \rightarrow Z, concluding Y→∼ZY \rightarrow \sim Z.
This exposes the flawed structural mapping of the fourth stimulus, noting that 'no A is B if C' translates to 'If C, then not B'.

Key Concept

Parallel Conditional Logic
Question 8Question →

A moral theory is considered practically useful only if it provides clear guidelines for daily action. Providing clear guidelines for daily action requires the theory to be based on universally recognizable human experiences. Therefore, any moral theory that is based on universally recognizable human experiences must be considered practically useful.

Which one of the following arguments exhibits a flawed pattern of reasoning most parallel to that exhibited in the argument above?

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Answer: A software system is deemed secure only if it undergoes rigorous penetration testing. Undergoing rigorous penetration testing requires a dedicated budget for independent auditors. Hence, any software system with a dedicated budget for independent auditors must be deemed secure.

Answer

The argument concluding that any software system with a dedicated budget must be deemed secure.
The correct answer exactly mimics the flawed structure of the stimulus. The stimulus establishes a transitive chain: A is sufficient for B, and B is sufficient for C (A -> B -> C). It then erroneously concludes that C is sufficient for A (C -> A). The correct choice establishes that Secure (S) requires Testing (T), and Testing (T) requires Budget (B). This creates the chain S -> T -> B. It then erroneously concludes that having a Budget (B) is sufficient to be Secure (S). This is a perfect match for the Illegal Reversal of the full chain.

Step-by-Step Solution

1
Analyze the logical structure of the stimulus premises.
Premise 1: Practically Useful (PU) -> Clear Guidelines (CG). Premise 2: Clear Guidelines (CG) -> Universally Recognizable (UR).
Translating indicator words ('only if', 'requires') into formal sufficient-necessary conditions is the first step in parallel conditional reasoning.
2
Analyze the logical structure of the stimulus conclusion and identify the flaw.
Conclusion: Universally Recognizable (UR) -> Practically Useful (PU). Flaw: Illegal Reversal of the transitive chain.
The stimulus chains A -> B and B -> C to form A -> C, but the conclusion illegally reverses this to C -> A.
3
Evaluate the options to find an identical flawed structure (A -> B, B -> C, therefore C -> A).
The correct option correctly translates to: Secure (S) -> Testing (T), Testing (T) -> Budget (B), Therefore Budget (B) -> Secure (S).
Parallel reasoning questions require matching the exact premises, conclusion sequence, and logical flaw present in the stimulus.

Key Concept

Parallel Flaw - Illegal Reversal of a Transitive Chain
Question 9Question →

Analyze the stimulus argument and the candidate argument provided below.

Stimulus: If the museum secures additional funding, it will open a new exhibit. The museum will attract more tourists only if it opens a new exhibit. Therefore, if the museum secures additional funding, it will attract more tourists.

Candidate Argument: If the author publishes a new novel, she will go on a book tour. The author will go on a book tour only if she receives a literary award. Thus, if the author publishes a new novel, she will receive a literary award.

Evaluate the following statement: The candidate argument exhibits a pattern of conditional reasoning that is structurally parallel to the stimulus argument.

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Answer: False

Answer

False
The statement is false because the two arguments do not share the same logical structure. The stimulus argument is flawed, incorrectly concluding a conditional relationship between two sufficient conditions. In contrast, the candidate argument is a valid transitive deduction.

Step-by-Step Solution

1
Analyze the formal logical structure of the stimulus argument.
Premise 1: Funding → Exhibit. Premise 2: Tourists → Exhibit ('only if' introduces the necessary condition). Conclusion: Funding → Tourists.
To determine the pattern of reasoning, we must translate the statements into formal conditional logic.
2
Evaluate the validity of the stimulus argument.
The argument is flawed. It presents two sufficient conditions (Funding, Tourists) for the same necessary condition (Exhibit) but incorrectly concludes that one sufficient condition leads to the other.
Parallel reasoning requires matching both the structural skeleton and the validity of the argument.
3
Analyze the logical structure and validity of the candidate argument.
Premise 1: Novel → Tour. Premise 2: Tour → Award. Conclusion: Novel → Award. This is a valid transitive deduction.
We must map the candidate's structure to compare it against the stimulus.
4
Compare the two logical structures to determine if they are parallel.
The stimulus is a flawed argument (A → B, C → B, therefore A → C), while the candidate is a valid transitive chain (A → B, B → C, therefore A → C).
Because their logical structures and validities differ fundamentally, they are not parallel.

Key Concept

Parallel Conditional Logic
Question 10Question →

Proper preservation of the newly discovered frescoes requires maintaining strict humidity controls in the gallery. However, the gallery's ancient wooden ceiling will avoid structural damage only if strict humidity controls are not maintained. Consequently, if the newly discovered frescoes are properly preserved, the gallery's ancient wooden ceiling will suffer structural damage.

The reasoning in the argument above is most similar to that in which one of the following?

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Answer: Successful cultivation of the rare orchid demands highly acidic soil. Yet, the native ferns in the same greenhouse will thrive only if the soil is not highly acidic. Therefore, if the rare orchids are successfully cultivated, the native ferns will not thrive.

Answer

The argument demonstrating that successful cultivation of the rare orchid leads to the native ferns not thriving.
The stimulus follows this exact pattern: Condition X requires Condition Y. Condition Z occurs only if Condition Y does NOT occur. Therefore, if Condition X occurs, Condition Z will NOT occur (because Z's necessary condition is blocked). The correct answer choice perfectly mirrors this: Orchid cultivation (X) requires acidic soil (Y). Ferns thriving (Z) happens only if there is no acidic soil (not Y). Therefore, Orchid cultivation (X) guarantees ferns will not thrive (not Z). Both arguments are logically valid and share the same absolute modal certainty.

Step-by-Step Solution

1
Diagram the conditional premises of the stimulus.
Premise 1: Frescoes Preserved (FP) -> Strict Humidity Controls (SHC). Premise 2: Avoid Damage (AD) -> NOT Strict Humidity Controls (~SHC).
To reveal the underlying logical framework used to reach the conclusion.
2
Diagram the conclusion of the stimulus.
Conclusion: Frescoes Preserved (FP) -> Suffer Damage (~AD).
To identify the exact relationship drawn from the premises.
3
Identify the logical operation used to connect the premises.
By taking the contrapositive of Premise 2 (SHC -> ~AD), we can form a valid transitive chain: FP -> SHC -> ~AD.
Understanding how the conclusion was validly derived is necessary to find its structural parallel.
4
Evaluate the answer choices to find the exact same structure (A -> B; C -> ~B; Conclusion: A -> ~C) with identical absolute modal strength.
The correct argument translates to: Rare Orchid (RO) -> Highly Acidic (HA); Ferns Thrive (FT) -> ~HA. Conclusion: RO -> ~FT. This is structurally isomorphic to the stimulus.
Parallel reasoning requires matching the formal logic symbols and the certainty level exactly.

Key Concept

Parallel Conditional Logic involving transitive chains and contrapositives.
Question 11Question →

If the tech startup's software is truly innovative, it will secure venture capital funding. However, the startup will not secure venture capital funding unless its founders have a proven track record. Therefore, if the tech startup's software is truly innovative, its founders must have a proven track record.

Which of the following arguments is most similar in its pattern of reasoning to the argument above?

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Answer: If the telescope's mirror is perfectly aligned, the images of the nebula will be exceptionally sharp. The images of the nebula will not be exceptionally sharp unless the atmospheric conditions are optimal. Therefore, if the telescope's mirror is perfectly aligned, the atmospheric conditions must be optimal.

Answer

The argument concerning the telescope's mirror, sharp images, and atmospheric conditions.
The correct answer accurately mirrors the stimulus by presenting a valid transitive chain. It establishes a sufficient condition leading to a necessary outcome (Aligned -> Sharp), introduces a second necessary condition using 'unless' (Sharp -> Optimal), and validly concludes that the initial sufficient condition guarantees the final necessary condition (Aligned -> Optimal).

Step-by-Step Solution

1
Map the formal conditional structure of the stimulus.
Premise 1 translates to: Innovative -> Funding. Premise 2 uses 'unless', which translates to 'if not'. So, Not Track Record -> Not Funding, which forms the contrapositive: Funding -> Track Record.
Identifying the exact logical components is necessary for parallel reasoning.
2
Determine the validity and conclusion format of the stimulus.
The premises form a valid transitive chain: Innovative -> Funding -> Track Record. The conclusion (Innovative -> Track Record) validly follows with absolute certainty ('must').
A parallel argument must replicate the validity, chain structure, and modal strength of the original.
3
Evaluate the answer choices to find the exact structural match.
The telescope argument maps to: Aligned -> Sharp; Not Optimal -> Not Sharp (Sharp -> Optimal); Conclusion: Aligned -> Optimal. This perfectly matches the valid transitive structure and absolute certainty.
This is the only choice that does not introduce a logical flaw or alter the degree of certainty.

Key Concept

Parallel Conditional Logic using Transitive Chains and the word 'unless'
Question 12Question →

Analyze the following natural language arguments concerning interstellar mission protocols. Match each argument to its exact underlying formal symbolic conditional structure. Let the variables XX, YY, and ZZ represent the distinct conditions or events in the order they logically appear.

Click a left item, then click its matching right item

Items

A spacecraft can initiate the landing sequence only if it has cleared the debris field. The debris field will not be cleared unless the shield generator is fully operational. Thus, if a spacecraft lacks a fully operational shield generator, it cannot initiate the landing sequence.
Approval from the science directorate is required for commencing the drilling operation. Approval from the science directorate requires submission of a hazard report. Therefore, if a hazard report has been submitted, the drilling operation will commence.
The crew will experience optimal gravity only if the rotation module is engaged. The rotation module will be engaged only if the primary reactor is functioning. The primary reactor is currently offline. Thus, the crew will not experience optimal gravity.
If the navigation sensors detect an anomaly, the main thrusters will automatically shut down. The main thrusters shutting down will cause the auxiliary beacons to activate. The navigation sensors did not detect an anomaly. Thus, the auxiliary beacons will not activate.

Matches

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Answer

The arguments logically map as follows: the landing sequence argument features a contrapositive chain; the drilling operation argument features an illegal reversal flaw; the gravity argument features a valid modus tollens deduction; and the navigation sensors argument features an illegal negation flaw.
Each natural language argument uniquely translates into one of the provided formal skeletons based on strict syntactic indicators ('only if', 'unless', 'requires', 'causes'). Carefully mapping the sufficient and necessary conditions reveals two flawed arguments (one illegal reversal, one illegal negation) and two valid deductions (one contrapositive, one modus tollens chain).

Step-by-Step Solution

1
Translate the 'landing sequence' argument into formal logic.
X -> Y, ~Z -> ~Y. Conclusion: ~Z -> ~X.
Understanding 'only if' as introducing a necessary condition, and 'unless' as 'if not' reveals the valid conditional chain.
2
Translate the 'drilling operation' argument into formal logic.
X -> Y, Y -> Z. Conclusion: Z -> X.
Identifying 'is required for' and 'requires' helps spot the illegal reversal flaw where the conclusion reverses the established sufficient-necessary relationship.
3
Translate the 'optimal gravity' argument into formal logic.
X -> Y, Y -> Z, ~Z. Conclusion: ~X.
Chaining the two 'only if' statements creates a transitive path. Denying the final necessary condition (~Z) validly denies the initial sufficient condition (~X).
4
Translate the 'navigation sensors' argument into formal logic.
X -> Y, Y -> Z, ~X. Conclusion: ~Z.
The chain is established by 'if' and 'cause'. The premise denies the initial sufficient condition (~X) to wrongly deny the final necessary condition (~Z), which is an illegal negation.

Key Concept

Parallel Conditional Logic
Estimated Time:2m 30s
Question 13Question →

Target Argument: A commercial spacecraft is cleared for launch only if its primary propulsion system passes a rigorous stress test. Passing this stress test requires that all fuel valves be completely free of micro-fractures. Consequently, any spacecraft whose fuel valves contain micro-fractures will not be cleared for launch.

Candidate Argument: No medical diagnostic algorithm is approved for clinical use unless it is validated on a diverse patient dataset. Validation on a diverse patient dataset is impossible without the explicit consent of multiple hospital networks. Thus, any diagnostic algorithm that has not been approved for clinical use must lack the explicit consent of multiple hospital networks.

Statement: The Candidate Argument exhibits a pattern of reasoning that is logically parallel to that of the Target Argument.

Show answer & explanation

Answer: False

Answer

False
The correct answer is False because the two arguments differ fundamentally in their logical validity. The Target Argument forms a valid transitive chain (Cleared -> Passes -> Free of fractures) and correctly draws a contrapositive conclusion (~Free of fractures -> ~Cleared). In contrast, the Candidate Argument builds a structurally similar chain (Approved -> Validated -> Consent) but draws an invalid conclusion by illegally negating the sufficient condition (~Approved -> ~Consent). An invalid argument is never logically parallel to a valid one.

Step-by-Step Solution

1
Translate the Target Argument into formal conditional logic.
Premise 1: Cleared for launch (C) -> Passes stress test (P). Premise 2: Passes stress test (P) -> Free of micro-fractures (F). Chain: C -> F. Conclusion: Contains micro-fractures (~F) -> Not cleared (~C).
To establish the underlying logical skeleton and assess the validity of the Target Argument.
2
Evaluate the validity of the Target Argument.
The conclusion (~F -> ~C) is the valid contrapositive of the derived premise chain (C -> F). The Target Argument is structurally valid.
A candidate argument can only be logically parallel if it matches both the structural pattern and the validity of the target.
3
Translate the Candidate Argument into formal conditional logic.
Premise 1: Approved (A) -> Validated (V). Premise 2: Validated (V) -> Consent (C). Chain: A -> C. Conclusion: Not approved (~A) -> Lacks consent (~C).
To map the Candidate Argument's structure, looking past surface-level linguistic similarities.
4
Evaluate the validity of the Candidate Argument and compare it to the Target Argument.
The Candidate Argument's conclusion (~A -> ~C) incorrectly negates the sufficient condition, committing an illegal negation flaw. Because the Target Argument is valid and the Candidate Argument is flawed, they are not logically parallel.
Arguments with divergent logical validities cannot be considered parallel in reasoning.

Key Concept

Parallel Conditional Logic
Estimated Time:2m 0s
Question 14Question →

Analyze the natural language arguments below and match each to its precise formal symbolic structure. Use variables XX, YY, and ZZ to represent the distinct conditions in the order they appear.

Click a left item, then click its matching right item

Items

If the chemical plant reduces its emissions, the local water quality will improve. Furthermore, the endangered fish population will recover if the water quality improves. The chemical plant clearly did not reduce its emissions, because the fish population is not recovering.
Class sizes will not decrease. After all, the university decided against increasing tuition. Yet we know that if tuition increases, more faculty can be hired, and if more faculty are hired, class sizes decrease.
If the new software is intuitive, employees will adopt it quickly. A rapid adoption rate guarantees that overall productivity will rise. Thus, since overall productivity has indeed risen, the new software must be intuitive.
The governor signed the bill. Since signing the bill ensures the transportation budget will expand, and an expanded budget means the highway repair project will begin, the highway project will definitely begin.

Matches

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Answer

The chemical plant argument is a Valid Contrapositive. The university tuition argument is an Invalid Negation. The software argument is an Invalid Reversal. The governor argument is a Valid Transitive chain.
Each natural language argument corresponds exactly to one symbolic representation by mapping its sufficient and necessary conditions in order. The correct match depends on whether the given premise affirms or denies either the beginning or the end of the conditional chain.

Step-by-Step Solution

1
Translate the 'chemical plant' argument into symbolic logic.
Plant reduces (XX) →\rightarrow Water improves (YY). Water improves (YY) →\rightarrow Fish recover (ZZ). Fact: Fish do not recover (∼Z\sim Z). Conclusion: Plant did not reduce (∼X\sim X).
Tracking the argument formally reveals a valid application of the contrapositive across a conditional chain.
2
Translate the 'university tuition' argument into symbolic logic.
Tuition increases (XX) →\rightarrow Faculty hired (YY). Faculty hired (YY) →\rightarrow Class sizes decrease (ZZ). Fact: Tuition does not increase (∼X\sim X). Conclusion: Class sizes will not decrease (∼Z\sim Z).
This highlights the logical flaw of illegal negation, as the absence of a sufficient condition does not guarantee the absence of a necessary condition.
3
Translate the 'new software' argument into symbolic logic.
Software intuitive (XX) →\rightarrow Adopted quickly (YY). Adopted quickly (YY) →\rightarrow Productivity rises (ZZ). Fact: Productivity rose (ZZ). Conclusion: Software intuitive (XX).
This uncovers the flaw of illegal reversal, where affirming a necessary condition is incorrectly used to deduce that the sufficient condition was met.
4
Translate the 'governor bill' argument into symbolic logic.
Signs bill (XX) →\rightarrow Budget expands (YY). Budget expands (YY) →\rightarrow Project begins (ZZ). Fact: Signs bill (XX). Conclusion: Project begins (ZZ).
This represents a straightforward, valid transitive chain application (Modus Ponens) moving from a sufficient trigger to the ultimate necessary outcome.

Key Concept

Parallel Conditional Logic
Question 15Question →

If a medical device is to be approved for surgical use, it must undergo three distinct phases of clinical trials. However, any device that relies primarily on experimental nanomaterials will not be permitted to undergo three distinct phases of clinical trials. Therefore, devices relying primarily on experimental nanomaterials will not be approved for surgical use.

Which one of the following arguments exhibits a pattern of reasoning most logically parallel to that of the argument above?

Show answer & explanation

Answer: If a chef is to earn a prestigious culinary award, the restaurant must offer an original tasting menu. But any restaurant operating out of a temporary pop-up space cannot offer an original tasting menu. Thus, temporary pop-up spaces will never earn a prestigious culinary award.

Answer

The correct answer is the argument about the chef, culinary awards, and pop-up spaces.
The correct answer accurately mirrors the logically valid structure of the stimulus. The stimulus argues that achieving a goal (A) requires a condition (B), a certain entity (C) cannot meet condition (B), and thus entity (C) cannot achieve goal (A). The credited choice perfectly replicates this: achieving the culinary award (A) requires a tasting menu (B), pop-up spaces (C) cannot offer a tasting menu (B), so pop-up spaces (C) cannot achieve the award (A).

Step-by-Step Solution

1
Map the formal logic of the stimulus.
Premise 1: Approved -> 3 Phases. Premise 2: Nanomaterials -> NOT 3 Phases. Conclusion: Nanomaterials -> NOT Approved.
Identifying the abstract skeleton of the argument is essential for finding an exact structural match.
2
Analyze the validity of the stimulus.
The argument is valid. It relies on the contrapositive of Premise 1 (NOT 3 Phases -> NOT Approved) combined with Premise 2.
A parallel argument must match the exact validity (valid or flawed) of the original stimulus.
3
Evaluate the options against the established structural map.
The culinary award argument translates to: Premise 1: Award -> Tasting Menu. Premise 2: Pop-up -> NOT Tasting Menu. Conclusion: Pop-up -> NOT Award. This perfectly mirrors the stimulus.
Eliminating arguments with different structures or logical flaws isolates the correct parallel reasoning.

Key Concept

Parallel Conditional Logic involving a valid contrapositive deduction.
Question 16Question →

Consider the formal logic utilized in the following two arguments:

Argument A: A city will be selected to host the global summit only if it significantly upgrades its public transportation network. The city of Oakhaven has significantly upgraded its public transportation network. Therefore, Oakhaven will be selected to host the global summit.

Argument B: Only if a patient strictly adheres to the prescribed dietary regimen will the new therapeutic protocol be effective. The patient in Ward 4 did not strictly adhere to the prescribed dietary regimen. Therefore, the new therapeutic protocol will not be effective for this patient.

Statement: The logical structure of Argument B exactly parallels the logical structure of Argument A.

Show answer & explanation

Answer: False

Answer

The statement is false because the two arguments differ fundamentally in their logical validity.
The statement is false because the arguments have fundamentally different logical structures. Argument A commits a Mistaken Reversal (treating the necessary condition 'upgrades network' as sufficient), while Argument B executes a logically valid Modus Tollens deduction (denying the necessary condition 'adheres to diet' to conclude the sufficient condition 'will be effective' cannot occur).

Step-by-Step Solution

1
Diagram the conditional structure of Argument A.
Host Summit -> Upgrade Transit. Premise: Upgrade Transit. Conclusion: Host Summit.
To identify if Argument A is a valid deduction or a formal fallacy.
2
Evaluate the validity of Argument A.
Argument A exhibits a Mistaken Reversal. It affirms the necessary condition (upgrading transit) to improperly conclude that the sufficient condition (hosting the summit) is met.
Identifying the specific flaw is necessary to find a parallel structural match.
3
Diagram the conditional structure of Argument B.
Protocol Effective -> Adhere to Diet. Premise: Did NOT Adhere. Conclusion: Protocol NOT Effective.
To determine the formal logic pattern of the second argument.
4
Evaluate the validity of Argument B.
Argument B is a valid application of Modus Tollens (the contrapositive). It properly denies the necessary condition to conclude the sufficient condition cannot occur.
To compare its structural validity to Argument A.
5
Compare the structures to determine if they are parallel.
Since Argument A is a flawed argument (Mistaken Reversal) and Argument B is a valid argument (Modus Tollens), they are not structurally parallel.
Parallel reasoning questions require the arguments to have identical formal structures and matching validities.

Key Concept

Parallel reasoning requires identical formal structures. Two arguments cannot be logically parallel if one is structurally valid and the other is structurally flawed, regardless of surface similarities in indicator phrasing (like 'only if').
Estimated Time:1m 30s
Question 17Question →

A logging syndicate is granted access to the restricted reserve only if it employs sustainable harvesting techniques and passes an ecological impact audit. Passing this audit requires submitting a comprehensive wildlife protection plan. Apex Timber has not submitted a comprehensive wildlife protection plan. Thus, Apex Timber will definitely not be granted access to the restricted reserve.

Which of the following arguments is most similar in its pattern of reasoning to the argument above?

Show answer & explanation

Answer: A museum will restore a Renaissance canvas only if it secures specialized funding and hires a master conservator. Hiring a master conservator necessitates paying an international relocation fee. The museum cannot pay the international relocation fee. Thus, the museum will definitely not restore the Renaissance canvas.

Answer

The correct answer is the argument concerning the museum restoring a Renaissance canvas, as it perfectly replicates the logical structure and conclusion modality of the original argument.
The correct argument perfectly tracks the logical structure of the stimulus. It presents a necessary compound condition ('only if it secures specialized funding and hires a master conservator'), chains a part of that condition to a further requirement ('necessitates paying an international relocation fee'), denies that final requirement ('cannot pay...'), and validly concludes that the initial sufficient condition is entirely denied ('will definitely not restore').

Step-by-Step Solution

1
Diagram the formal logic of the stimulus.
Access granted -> (Sustainable techniques AND Passes audit). Passes audit -> Submits plan. Apex Timber did NOT submit plan. Conclusion: Apex Timber is NOT granted access.
Identifying the precise conditional relationships is required to find an identical structure.
2
Characterize the validity and modality of the stimulus.
The argument uses a valid Modus Tollens deduction across a nested conditional chain. The conclusion is framed with absolute certainty ('will definitely not').
A parallel argument must match not just the conditional structure, but also its logical validity and degree of certainty.
3
Evaluate the answer choices to find the exact structural match.
The museum argument dictates: Restore -> (Funding AND Conservator). Conservator -> Fee. No Fee. Conclusion: No Restore. This is a perfect match.
The correct option must replicate the 'A -> (B and C)', 'C -> D', 'Not D -> Not A' structure without introducing logical flaws.

Key Concept

Parallel Conditional Logic
Question 18Question →

Stimulus Argument: If a coral reef is to fully recover from a severe bleaching event, it must be situated in a region with stable ocean temperatures. However, no reef can maintain stable ocean temperatures unless it is shielded from the primary equatorial currents. Thus, any coral reef that fully recovers from a severe bleaching event must be shielded from the primary equatorial currents.

Candidate Argument: If a newly published novel is to win the prestigious Sterling Prize, it must have sold over a million copies. Furthermore, a novel can sell over a million copies only if it has been adapted into a major motion picture. Therefore, any novel that has been adapted into a major motion picture will win the prestigious Sterling Prize.

Statement: The pattern of reasoning in the candidate argument is logically parallel to the pattern of reasoning in the stimulus argument.

Show answer & explanation

Answer: False

Answer

False. The arguments are not logically parallel because the stimulus argument is valid, while the candidate argument commits a formal logical flaw.
The statement is false because the two arguments possess fundamentally different logical structures regarding their conclusions. The stimulus presents a valid transitive deduction (A → B, B → C, therefore A → C). While the candidate argument shares the premise structure (X → Y, Y → Z), it draws a flawed conclusion (Z → X), representing an illegal reversal.

Step-by-Step Solution

1
Translate the stimulus argument into formal conditional logic.
Premise 1: Fully Recover → Stable Temperatures. Premise 2: Stable Temperatures → Shielded ('no B unless C' translates to B → C). Conclusion: Fully Recover → Shielded.
To identify the exact structural template and establish that the stimulus utilizes a valid transitive chain (A → B, B → C, therefore A → C).
2
Translate the candidate argument into formal conditional logic.
Premise 1: Win Prize → Million Copies. Premise 2: Million Copies → Adapted ('Y only if Z' translates to Y → Z). Conclusion: Adapted → Win Prize.
To map the candidate's logical flow and prepare it for structural comparison against the stimulus.
3
Compare the logical structures of the two arguments.
The stimulus correctly deduces A → C from its premises. The candidate incorrectly deduces C → A from its premises, reversing the sufficient and necessary conditions.
An argument containing a logical flaw (illegal reversal) cannot be parallel to an argument that is logically valid.

Key Concept

Parallel Conditional Logic: Analyzing and matching the formal symbolic structure and validity of natural language arguments, paying careful attention to the directionality of conditional conclusions.
Parallel Conditional Logic Practice Questions — LSAT | Examkin