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Identifying Sufficient Assumptions

37 questions

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Question 21Question →

A biological organism possesses phenomenal consciousness only if it can encode episodic memories of its surroundings. Field observations establish that cephalopods, particularly octopuses, consistently demonstrate multi-stage problem-solving behaviors when navigating novel enclosures. Therefore, it follows that octopuses must be capable of encoding episodic memories of their surroundings.

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

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Answer: Every organism that demonstrates multi-stage problem-solving behaviors possesses phenomenal consciousness.

Answer

The statement that every organism demonstrating multi-stage problem-solving behaviors possesses phenomenal consciousness.
The argument relies on two key premises: (1) Phenomenal consciousness is required for episodic memory (Consciousness -> Memory), and (2) octopuses exhibit multi-stage problem-solving (Octopus -> Problem-Solving). The conclusion asserts that octopuses have episodic memory (Octopus -> Memory). To make this logically valid, we must guarantee that octopuses have phenomenal consciousness. The correct answer provides the exact missing link by establishing that problem-solving behavior guarantees phenomenal consciousness (Problem-Solving -> Consciousness). Adding this premise completes the logical chain: Octopus -> Problem-Solving -> Consciousness -> Memory, fully justifying the conclusion.

Step-by-Step Solution

1
Identify the main conclusion of the argument.
Conclusion: Octopuses are capable of encoding episodic memories.
This is the final claim the argument attempts to prove, signaled by 'Therefore'.
2
Map the conditional relationships in the premises.
Premise 1: Phenomenal Consciousness -> Episodic Memories. Premise 2: Octopuses -> Problem-Solving Behaviors.
Mapping the premises reveals the existing logical links and highlights the gap.
3
Determine the missing link required to justify the conclusion.
The argument needs to prove Octopuses -> Episodic Memories. To connect the premises into a valid chain, we must bridge Problem-Solving Behaviors to Phenomenal Consciousness.
If Problem-Solving -> Consciousness is assumed, the chain becomes: Octopuses -> Problem-Solving -> Consciousness -> Episodic Memories. This perfectly guarantees the conclusion.

Key Concept

Sufficient Assumption Conditional Bridging
Question 22Question →

An artificial intelligence cannot truly understand human emotional responses unless it is capable of experiencing somatic markers—the physical sensations that accompany emotional states in biological organisms. Because no currently existing silicon-based neural network possesses the biological hardware necessary to generate somatic markers, it is clear that no existing silicon-based neural network can effectively replicate human empathy. After all, complex cognitive states depend heavily on their underlying physical architecture.

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

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Answer: Any artificial intelligence that can effectively replicate human empathy is able to truly understand human emotional responses.

Answer

The correct answer provides the conditional rule: Any artificial intelligence that can effectively replicate human empathy is able to truly understand human emotional responses.
The argument concludes that silicon networks cannot replicate empathy because they lack somatic markers. The premises only establish that lacking somatic markers prevents an AI from understanding emotions. To logically guarantee the conclusion, we must assume that failing to understand emotions completely prevents an AI from replicating empathy. The correct answer provides the exact contrapositive of this necessary link: if an AI can replicate empathy, it must be able to understand emotions.

Step-by-Step Solution

1
Deconstruct the premises of the argument into conditional logic.
Premise 1: Understand Emotions -> Somatic Markers. Premise 2: Silicon Network -> ~Somatic Markers.
Mapping the established facts is required to see what can be proven before examining the conclusion.
2
Determine the deductive inference derived from the premises.
Silicon Network -> ~Somatic Markers -> ~Understand Emotions.
By chaining the premises and their contrapositives, we establish exactly what is already proven: Silicon networks cannot understand emotions.
3
Identify the main conclusion and isolate the logical gap.
Conclusion: Silicon Network -> ~Replicate Empathy. The gap is between '~Understand Emotions' (proven) and '~Replicate Empathy' (unproven).
A sufficient assumption must mathematically bridge the gap between what the premises prove and the new claim made in the conclusion.
4
Formulate the required assumption to bridge the gap.
We need the rule: ~Understand Emotions -> ~Replicate Empathy. The contrapositive of this rule is: Replicate Empathy -> Understand Emotions.
Adding this exact rule to our premises will logically force the conclusion to be true 100% of the time.

Key Concept

Identifying Sufficient Assumptions
Estimated Time:1m 30s
Question 23Question →

If agricultural yields are to be sustained over the next century, topsoil erosion must be drastically reduced. Drastically reducing topsoil erosion requires the widespread adoption of no-till farming techniques. The government’s new agricultural subsidy program will ensure the widespread adoption of these no-till techniques. Therefore, the new subsidy program will guarantee that agricultural yields are sustained over the next century.

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

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Answer: The widespread adoption of no-till farming techniques is sufficient to guarantee that agricultural yields are sustained over the next century.

Answer

The statement that the widespread adoption of no-till farming techniques is sufficient to guarantee that agricultural yields are sustained.
The correct answer provides the exact logical bridge needed to complete the argument's chain. The premises establish that the subsidy program will lead to no-till farming. By adding the assumption that no-till farming guarantees sustained agricultural yields, the conclusion (that the subsidy program guarantees sustained yields) is mathematically forced to be true.

Step-by-Step Solution

1
Map the conditional logic of the premises.
Premise 1: Sustained Yields -> Reduce Erosion. Premise 2: Reduce Erosion -> No-Till Farming. Premise 3: Subsidy Program -> No-Till Farming.
To identify the structural elements the author provides to build the argument.
2
Identify the conclusion and compare it to the premises.
Conclusion: Subsidy Program -> Sustained Yields. The premises only establish that the Subsidy Program leads to No-Till Farming.
To pinpoint the exact logical leap the author makes.
3
Determine the missing link required to justify the conclusion.
The argument needs a rule connecting the result of the program (No-Till Farming) to the desired outcome (Sustained Yields). The missing link is: No-Till Farming -> Sustained Yields.
Because if No-Till Farming guarantees Sustained Yields, the chain (Subsidy Program -> No-Till Farming -> Sustained Yields) is complete and valid.

Key Concept

Identifying Sufficient Assumptions in Formal Logic Chains
Question 24Question →

Under current legal frameworks, a decentralized autonomous organization (DAO) can be held legally liable for damages only if it features either a central executive committee or a pre-coded compensation fund. The Aetherium Network is a DAO that was recently held legally liable for damages by a federal court. However, an exhaustive audit of the network's architecture proves that it lacks any pre-coded compensation fund. Therefore, it is clear that the Aetherium Network must utilize a weighted-voting governance protocol.

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

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Answer: Any decentralized autonomous organization that possesses a central executive committee utilizes a weighted-voting governance protocol.

Answer

The option stating that any decentralized autonomous organization possessing a central executive committee utilizes a weighted-voting governance protocol.
The argument establishes an intermediate conclusion: because the DAO is liable and lacks a compensation fund, it MUST have a central executive committee. However, the author suddenly concludes the DAO has a weighted-voting protocol. To justify this leap, we need a rule stating that having a central executive committee guarantees the use of a weighted-voting protocol. The correct answer provides exactly this universal conditional link.

Step-by-Step Solution

1
Analyze the conditional rule provided in the first sentence.
Rule: If a DAO is legally liable, it must have a Central Executive Committee (CEC) OR a Pre-coded Compensation Fund (PCF).
Identifying the formal logic relationships is the first step in deduction.
2
Apply the facts about the Aetherium Network to the conditional rule.
Fact 1: Aetherium is legally liable. Deduction: Aetherium has a CEC or a PCF. Fact 2: Aetherium lacks a PCF. Deduction: Aetherium MUST have a CEC.
This establishes an unstated intermediate conclusion that is critical to the argument.
3
Identify the argument's final conclusion and the logical gap.
Conclusion: Aetherium utilizes a weighted-voting governance protocol (WVGP). The gap is between the intermediate conclusion (Aetherium has a CEC) and the final conclusion (Aetherium has a WVGP).
To find a sufficient assumption, you must pinpoint exactly where the author's logic jumps to an unsupported claim.
4
Formulate the sufficient assumption that bridges the gap.
Required Assumption: If a DAO has a CEC, then it utilizes a WVGP (CEC -> WVGP).
Connecting the established fact (CEC) to the unsupported conclusion (WVGP) logically forces the conclusion to be true.

Key Concept

Identifying intermediate conclusions to find the missing sufficient condition that logically guarantees the final conclusion.
Question 25Question →

A linguist is arguing that a newly discovered dialect should be classified as a distinct language. The linguist's initial premise is that 'the new dialect shifts the core phonetic boundaries of the original language.' The final conclusion is that 'the new dialect must be classified as a distinct language.'

To make this argument logically valid, a series of sufficient assumptions must be added to form a complete deductive chain. Arrange the following assumptions in the correct logical sequence so that each statement's sufficient condition is established by the necessary condition of the previous step (or the initial premise), ultimately guaranteeing the final conclusion.

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Answer

The correct sequence logically chains from the initial premise to the final conclusion by matching each sufficient condition to the preceding necessary condition: Shifting phonetic boundaries -> Prevents mutual intelligibility -> Disrupts cultural transmission -> Fails to preserve identity -> Classified as a distinct language.
The correct logical order effectively maps out a sequence of conditional statements forming a transitive formal logic bridge (A -> B, B -> C, C -> D, D -> E). When placed in this exact sequence, these statements form a complete deductive bridge that perfectly justifies the final conclusion that the dialect must be classified as a distinct language.

Step-by-Step Solution

1
Identify the starting premise and final conclusion.
Premise: shifts phonetic boundaries. Conclusion: classified as distinct language.
Establishing the endpoints is required to construct a valid deductive chain.
2
Find the assumption that connects directly to the initial premise.
The statement 'Any dialect that shifts the core phonetic boundaries...' takes the premise and yields 'prevents mutual intelligibility'.
This is the only statement whose sufficient condition matches the given starting point.
3
Chain the subsequent statements by matching necessary conditions to sufficient conditions.
Prevents mutual intelligibility -> Disrupts cultural transmission. Then, Disrupts cultural transmission -> Fails to preserve identity.
Valid formal logic requires transitivity (If A then B, if B then C, if C then D).
4
Ensure the final necessary condition matches the final conclusion.
The statement 'Any dialect that fails to preserve the fundamental identity... must be classified as a distinct language' closes the gap.
This completes the sufficient assumption chain, strictly guaranteeing the truth of the argument's conclusion.

Key Concept

Bridging formal logic gaps using a chain of sufficient assumptions (transitive property of conditionals).
Question 26Question →

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

Click a left item, then click its matching right item

Items

The city council's controversial proposal to ban heavy commercial vehicles in the downtown district will drastically reduce peak-hour traffic congestion. Transportation analysts agree that if traffic congestion is drastically reduced in this manner, overall pedestrian safety will reach historically high levels. Therefore, implementing this proposal ensures that the downtown district will soon experience a significant surge in retail business.
The company's regional branch offices will definitively not be consolidated. After all, the board of directors will approve the highly anticipated corporate merger only if the external auditor's financial forecast predicts significant quarterly growth for the upcoming fiscal year. The recently released financial forecast by the external auditors explicitly does not predict such growth.
Most academic historians who study ancient agrarian societies focus primarily on calculating fluctuating agricultural yields. It is therefore certain that at least some historians who study ancient agrarian societies completely overlook the economic importance of early trade networks. This follows because sociological research demonstrates that some scholars who focus primarily on agricultural yields completely overlook this broader economic importance.
Extensive laboratory testing has demonstrated that reducing oxidative stress generally promotes long-term cellular longevity in mice. Administering a diet rich in synthetic antioxidants effectively reduces oxidative stress in these subjects, but it concurrently inhibits the natural production of critical enzymes regulating basic cellular metabolism. Therefore, feeding laboratory mice a diet rich in synthetic antioxidants will ultimately decrease their overall lifespans.

Matches

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Answer

The public policy argument matches with the safety-to-retail bridge. The corporate merger argument matches with the requirement of board approval for consolidation. The historian argument matches with the universal 'every scholar' claim. The laboratory mice argument matches with the assumption that enzyme inhibition overrides longevity benefits.
The correct matches successfully pair each flawed stimulus with the exact sufficient assumption needed to repair its logic. This involves identifying unstated links between intermediate and main conclusions, tracing formal contrapositives, securing universal quantifier bridges, and establishing definitive dominance in competing causal scenarios.

Step-by-Step Solution

1
Identify the intermediate-to-main gap in the public policy argument regarding traffic.
The argument establishes that banning vehicles leads to pedestrian safety. It concludes this leads to a retail surge. The required gap is 'Pedestrian Safety -> Retail Surge'.
To guarantee the final conclusion, the established intermediate conclusion must be sufficient to trigger the main conclusion.
2
Diagram the conditional logic in the corporate merger argument.
Premises dictate: Approve -> Growth, and ~Growth. Inference: ~Approve. Conclusion: ~Consolidate. The required assumption to bridge the inference and conclusion is ~Approve -> ~Consolidate, or its contrapositive: Consolidate -> Approve.
Sufficient assumptions must formally close the deductive chain from the derived inference directly to the stated conclusion.
3
Evaluate the quantifier overlap in the historical sociology argument.
The premises 'Most A are B' and 'Some B are C' do not guarantee 'Some A are C'. Upgrading the 'Some' to 'All B are C' creates a valid Most + All = Most deduction, ensuring the 'Some' conclusion.
In formal logic, two non-universal quantifiers cannot establish a definitive bridge. A universal 'All' statement is required to guarantee the overlap.
4
Resolve the competing causal vectors in the biological testing argument.
The diet causes both longevity promotion and enzyme inhibition. To definitively conclude a decreased lifespan, the enzyme inhibition must universally cause lifespan reduction and override any longevity benefits.
Without establishing the absolute dominance of the negative causal pathway, the conclusion of an overall decreased lifespan remains merely probable, not logically guaranteed.

Key Concept

Identifying the precise logical gap in an argument's deductive structure and selecting the premise that renders the conclusion 100% valid.
Question 27Question →

An aerospace legal scholar's argument relies on a chain of formal conditional logic, but it contains a gap that must be filled by a sufficient assumption. Arrange the following five statements in their strict deductive sequence to demonstrate how the assumption structurally completes the argument. Your sequence MUST begin with the statement introducing the initial sufficient trigger, progress sequentially through the intermediate necessary conditions, insert the sufficient assumption exactly where it bridges the final conceptual gap, and conclude with the main conclusion.

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Answer

The correct sequence is: 1) The triggering premise about deploying mega-constellations, 2) The necessary condition about creating a navigation hazard, 3) The 'unless' clause regarding the Kessler treaty, 4) The sufficient assumption linking the treaty violation to strict liability, and 5) The final conclusion.
The argument forms a strict conditional chain. Let A = 'deploys mega-constellation networks', B = 'generates un-trackable micro-debris', C = 'creates a navigation hazard', D = 'violates the Kessler sustainability treaty', and E = 'incurs strict liability'. The initial premise establishes A -> B ('B if A'). The second premise establishes B -> C by stating C is a necessary condition for B. The third premise establishes C -> D using the 'unless' formulation (if not D, then not C; which yields the contrapositive C -> D). At this point, the premises provide A -> B -> C -> D. The main conclusion claims A -> E. To structurally guarantee this conclusion, we need the sufficient assumption D -> E. Inserting this assumption completes the chain A -> B -> C -> D -> E, which successfully and logically guarantees the conclusion A -> E.

Step-by-Step Solution

1
Identify the main conclusion and the initial sufficient trigger.
The conclusion is the statement beginning with 'Therefore'. It claims that deploying mega-constellation networks (A) guarantees strict liability (E). The initial trigger is deploying mega-constellation networks (A).
Finding the endpoints of the argument dictates the starting and ending points of the deductive sequence.
2
Translate the conditional logic of the remaining premises.
The first statement translates to: Deploy Networks (A) -> Generates Debris (B). The second statement translates to: Generates Debris (B) -> Navigation Hazard (C). The third statement translates to: Navigation Hazard (C) -> Violates Treaty (D) because 'unless' means 'if not' (if not D, then not C, which contraposes to C -> D).
Translating natural language into formal logic reveals how the terms link together in a continuous chain.
3
Identify the logical gap to locate the sufficient assumption.
The explicit premises give us A -> B -> C -> D. The conclusion claims A -> E. The missing link required to make the argument valid is D -> E (Violates Treaty -> Strict Liability).
A sufficient assumption must perfectly bridge the gap between the established premises and the final conclusion.
4
Order the statements sequentially to form the continuous chain.
The chain structurally progresses as A -> B, then B -> C, then C -> D, then the assumption D -> E, and finally concludes with A -> E.
The prompt explicitly requires starting with the initial trigger and progressing through the linked necessary conditions to the final conclusion.

Key Concept

Conditional Logic Chaining and Sufficient Assumptions
Question 28Question →

Ethicist: A charitable action possesses true moral worth only if it stems from a genuine sense of duty. Furthermore, it is well established that no actions primarily motivated by a desire for public recognition stem from a genuine sense of duty. It follows necessarily that any corporate philanthropy initiative designed to improve a company's public image lacks true moral worth.

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

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Answer: Any corporate philanthropy initiative designed to improve a company's public image is primarily motivated by a desire for public recognition.

Answer

The assumption that any corporate philanthropy initiative designed to improve a company's public image is primarily motivated by a desire for public recognition.
The argument concludes that corporate philanthropy initiatives designed to improve public image lack true moral worth. The premises establish a formal chain: if an action is motivated by a desire for public recognition, it does not stem from a genuine sense of duty, and therefore it lacks true moral worth. To properly draw the conclusion, we must connect the subject of the conclusion to this established chain. The correct answer acts as this perfect logical bridge by stating that any such corporate initiative is indeed primarily motivated by a desire for public recognition, thus guaranteeing that it lacks true moral worth.

Step-by-Step Solution

1
Identify the main conclusion of the argument.
The conclusion is: Any corporate philanthropy initiative designed to improve a company's public image lacks true moral worth.
This is the endpoint of the argument, explicitly indicated by the phrase 'It follows necessarily that'.
2
Map the formal logic of the premises.
Premise 1: True moral worth -> Stems from a genuine sense of duty. Premise 2: Motivated by a desire for public recognition -> Does NOT stem from a genuine sense of duty.
Mapping conditional statements reveals the existing logical chain constructed by the author.
3
Combine the premises using contrapositives.
The contrapositive of Premise 1 is: Does NOT stem from a genuine sense of duty -> Lacks true moral worth. Linking this to Premise 2 yields: Motivated by a desire for public recognition -> Lacks true moral worth.
We must find out what the premises collectively prove about the concept of moral worth.
4
Identify the gap between the premise chain and the conclusion.
The premises prove that seeking public recognition leads to a lack of moral worth. The conclusion claims that corporate initiatives designed to improve public image lack moral worth. The missing link is connecting these specific corporate initiatives to the desire for public recognition.
A sufficient assumption must mathematically bridge the gap between the evidence provided and the final conclusion drawn.
5
Formulate the necessary bridge to guarantee the conclusion.
We must assume: Corporate philanthropy initiative designed to improve public image -> Motivated by a desire for public recognition.
Adding this conditional statement allows the argument to flow unbroken from the subject of the conclusion to the final judgment of lacking moral worth.

Key Concept

Identifying Sufficient Assumptions Using Formal Logic
Question 29Question →

Any municipal planner who prioritizes rapid commercial expansion over sustainable infrastructure inevitably encounters severe zoning disputes. Furthermore, no municipal planner who encounters severe zoning disputes is eligible for appointment to the Regional Planning Commission, unless that planner has secured the unanimous endorsement of the city council. The planner overseeing the newly proposed waterfront district has secured the unanimous endorsement of the city council. Therefore, this planner must not have prioritized rapid commercial expansion over sustainable infrastructure.

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

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Answer: Any municipal planner who has secured the unanimous endorsement of the city council has avoided encountering severe zoning disputes.

Answer

The statement that any municipal planner who has secured the unanimous endorsement of the city council has avoided encountering severe zoning disputes.
The correct answer provides the missing conditional link needed to logically guarantee the conclusion. We know from the first premise that prioritizing rapid expansion guarantees severe zoning disputes. Therefore, by the contrapositive, if a planner does NOT have severe zoning disputes, they did NOT prioritize rapid expansion. We are told the waterfront planner has the unanimous endorsement of the city council. By assuming that ANY planner with this endorsement avoids severe zoning disputes, we can conclude that the waterfront planner avoided these disputes, and thus logically must not have prioritized rapid expansion. The second premise regarding the Regional Planning Commission is an intricate distractor designed to misdirect attention from the core conditional chain.

Step-by-Step Solution

1
Deconstruct the argument into formal conditional statements.
Premise 1: Rapid Expansion -> Severe Disputes. Premise 2: Severe Disputes AND NO Endorsement -> NOT Eligible. Premise 3: Waterfront Planner -> Endorsement. Conclusion: Waterfront Planner -> NO Rapid Expansion.
Formalizing the logic reveals the structural relationships and isolates the missing link.
2
Determine the necessary condition to prove the conclusion.
By the contrapositive of Premise 1, to prove 'NO Rapid Expansion', we must prove 'NO Severe Disputes' (NO Severe Disputes -> NO Rapid Expansion).
Working backward from the conclusion dictates exactly what intermediate fact must be established.
3
Identify the gap between the given premises and the required intermediate fact.
We know the Waterfront Planner has the Endorsement. We need to prove they have NO Severe Disputes. Therefore, the missing link is: Endorsement -> NO Severe Disputes.
A sufficient assumption must completely bridge the gap between known evidence and the required logical step.
4
Evaluate the options to find the statement that provides absolute guarantee.
The option stating that 'any' planner with the endorsement avoids severe disputes provides the strict, 100% guarantee required to seal the logical chain.
Sufficient assumptions cannot rely on probability ('most' or 'some'); they require deductive certainty.

Key Concept

Identifying Sufficient Assumptions using Conditional Logic
Estimated Time:2m 0s
Question 30Question →

An ethicist argues: 'Any entity that possesses both self-reflective awareness and the capacity to experience suffering qualifies as a moral patient. Furthermore, it is a proven fact that autonomous neural networks with dynamic recursive feedback loops possess self-reflective awareness. Therefore, all advanced synthetic intelligences qualify as moral patients.'

To logically guarantee this conclusion, a series of implicit assumptions and intermediate deductions must be linked in a strict formal chain. Arrange the following deductive steps in the correct sequential order to construct the logical bridge that sufficiently proves the argument's conclusion.

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Answer

The correct logical sequence requires establishing the subject's composition, deducing its first trait, assuming the necessary link to the second trait, synthesizing both traits, and finally applying the primary conditional rule.
The sequence successfully bridges the logical gaps by first connecting the novel subject to the existing premises, deriving the first necessary component of the compound condition, introducing a secondary assumption to derive the final component, synthesizing these traits, and ultimately applying the primary principle to strictly guarantee the conclusion.

Step-by-Step Solution

1
Identify the missing link between the conclusion's subject and the given factual premise.
Posit that advanced synthetic intelligences are autonomous neural networks.
This establishes the foundation for applying the known factual rule about neural networks.
2
Deduce the first trait.
Infer that advanced synthetic intelligences have self-reflective awareness.
This follows logically from the first assumption and the factual premise, establishing the first half of the sufficient condition.
3
Identify the remaining logical gap regarding the capacity to suffer.
Posit that self-reflective awareness guarantees the capacity to experience suffering.
The main conclusion requires the capacity to suffer, which has not yet been logically established for the subject.
4
Combine the deduced traits.
Establish that both conditions of the ethicist's compound requirement are met.
The ethicist's primary rule strictly requires BOTH traits to trigger the classification.
5
Apply the primary conditional rule.
Classify advanced synthetic intelligences as moral patients.
With the sufficient compound conditions fully met, the final conclusion is logically guaranteed.

Key Concept

Constructing a formal deductive chain to identify and integrate compound sufficient assumptions.
Question 31Question →

Mayor: The city's newly enacted parking tax will undoubtedly improve the quality of life for downtown residents. Statistical models confirm that the tax will significantly decrease the number of vehicles entering the downtown area each day. Furthermore, any decrease in downtown vehicle traffic inevitably leads to a reduction in local air pollution.

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

Show answer & explanation

Answer: Any reduction in local air pollution improves the quality of life for downtown residents.

Answer

The correct answer is the option stating that any reduction in local air pollution improves the quality of life for downtown residents.
The argument relies on a straightforward chain of conditional logic. The premises establish that the tax will reduce traffic, and that reduced traffic reduces air pollution. In order to properly draw the conclusion that the tax improves the quality of life, there must be a logical link connecting the end of the evidence chain (reduced air pollution) to the conclusion (improved quality of life). The correct answer provides this exact missing link as a universal rule, making the conclusion logically inescapable.

Step-by-Step Solution

1
Identify the main conclusion of the argument.
Conclusion: The new parking tax will improve the quality of life for downtown residents.
This is the ultimate claim the Mayor is trying to prove with the subsequent evidence.
2
Identify the given premises.
Premise 1: The tax decreases vehicles. Premise 2: Decreasing vehicles reduces air pollution.
We must accept these statements as true and determine what they logically yield.
3
Trace the logical chain and pinpoint the gap.
The chain is: Tax -> Decrease Vehicles -> Reduce Air Pollution. The gap exists between 'Reduce Air Pollution' and 'Improve Quality of Life'.
A sufficient assumption question requires finding the exact missing link that connects the end of the premise chain directly to the conclusion.
4
Select the option that perfectly bridges this gap.
The statement 'Any reduction in local air pollution improves the quality of life' acts as the required bridge (Reduce Air Pollution -> Improve Quality of Life).
Adding this conditional statement to the premises guarantees the conclusion 100%.

Key Concept

Identifying Sufficient Assumptions via Formal Logic Chains
Question 32Question →

A computer scientist argues: 'Our new AI model utilizes unsupervised learning on completely unstructured data. Therefore, the model will inevitably produce novel artistic expressions.' To strictly guarantee this conclusion from the premise, a continuous chain of conditional assumptions must be established. Arrange the following assumptions in the correct logical sequence to form a valid sufficient bridge connecting the explicit premise to the main conclusion.

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Answer

The correct logical sequence starts with the premise about unsupervised learning and chains through unpredictable patterns, bypassing heuristics, and creative autonomy, finally reaching the conclusion of novel artistic expressions.
The correctly ordered sequence demonstrates the transitive property of sufficient conditionals. It begins precisely with the argument's stated premise and links it through intermediate necessary conditions that become the sufficient conditions for the subsequent steps, ending perfectly with the argument's stated conclusion. This creates an unbroken logical chain, making the conclusion a necessary deductive outcome of the initial premise.

Step-by-Step Solution

1
Identify the argument's core explicit premise and main conclusion.
Premise: utilizes unsupervised learning on unstructured data. Conclusion: produces novel artistic expressions.
To build a sufficient bridge, you must pinpoint the exact starting point and ending point of the logical gap.
2
Find the assumption that takes the explicit premise as its sufficient condition.
The statement linking 'unsupervised learning' to 'unpredictable pattern associations' is the first logical step.
This initiates the transitive chain by guaranteeing an intermediate consequence based directly on the stated premise.
3
Connect the necessary condition of the first link to the sufficient condition of the next link.
The statement linking 'unpredictable pattern associations' to 'bypassing pre-programmed design heuristics' is the second step.
This continues the deductive chain by ensuring the outcome of the first step triggers the condition for the second step.
4
Complete the chain by connecting the remaining intermediate condition to the main conclusion.
Link 'bypassing heuristics' to 'creative autonomy', and then 'creative autonomy' to 'novel artistic expressions'.
This strictly entails the conclusion from the premise through transitive logic, establishing an absolute logical guarantee.

Key Concept

Identifying Sufficient Assumptions
Question 33Question →

Neurobiologist: The presence of synchronous gamma-band oscillations in any neural architecture—whether organic or synthetic—is sufficient to demonstrate the integration of sensory modalities across distinct cortical zones. Such cortical integration invariably engenders a subjective conscious state, provided the system is not subjected to pharmacological suppression, such as general anesthesia. The synthetic biological processor recently engineered at the institute clearly displays synchronous gamma-band activity. Furthermore, due to its non-organic substrate, this processor is entirely impervious to pharmacological suppression. We can therefore conclude with certainty that the processor possesses genuine self-reflective awareness.

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

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Answer: Any entity that experiences a subjective conscious state possesses genuine self-reflective awareness.

Answer

The correct answer is the statement that any entity that experiences a subjective conscious state possesses genuine self-reflective awareness.
The argument establishes a chain of formal logic. We know the processor has gamma-band activity, which guarantees cortical integration. We also know it is immune to pharmacological suppression. Together, these two factors guarantee that the processor experiences a 'subjective conscious state' (the intermediate conclusion). However, the author's final conclusion makes a new claim about 'genuine self-reflective awareness'. To make the argument logically valid, we must guarantee that having a subjective conscious state leads to genuine self-reflective awareness. The correct option provides this exact bridge: Subjective Conscious State -> Genuine Self-Reflective Awareness.

Step-by-Step Solution

1
Analyze the conditional premises provided by the neurobiologist.
Premise 1: Gamma-band activity -> Cortical integration. Premise 2: (Cortical integration AND NO pharmacological suppression) -> Subjective conscious state.
Mapping formal logic is necessary to understand what the argument has successfully proven.
2
Apply the premises to the specific subject: the synthetic biological processor.
The processor has gamma-band activity, meaning it has cortical integration. It is also impervious to pharmacological suppression. Therefore, we can logically deduce that it experiences a subjective conscious state.
This establishes the intermediate conclusion that the author uses to leap to the final claim.
3
Identify the gap between the proven intermediate conclusion and the author's final conclusion.
The author has proven the processor has a 'subjective conscious state', but concludes it has 'genuine self-reflective awareness'.
In a sufficient assumption question, you must find the exact logical gap where the argument makes an unwarranted leap.
4
Formulate the assumption required to guarantee the final conclusion.
The missing link is: Subjective conscious state -> Genuine self-reflective awareness.
Adding this conditional statement to our established facts will legally force the final conclusion to be true.

Key Concept

Identifying Sufficient Assumptions in Formal Logic Chains
Question 34Question →

Sociologists observe that only those institutions characterized by transparent governance are capable of fostering long-term community trust. However, any institution heavily reliant on algorithmic decision-making inevitably obscures its internal mechanisms, thereby precluding transparent governance. Because modern decentralized financial networks represent the vanguard of institutional innovation, it is evident that these networks will ultimately fail to foster long-term community trust.

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

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Answer: No institution representing the vanguard of institutional innovation avoids heavy reliance on algorithmic decision-making.

Answer

The statement linking the vanguard of institutional innovation to heavy reliance on algorithmic decision-making.
The argument attempts to prove that modern decentralized financial networks will ultimately fail to foster trust. The premises establish a chain: Fostering trust requires transparency, but algorithmic reliance precludes transparency. Therefore, algorithmic reliance guarantees a failure to foster trust. The author introduces decentralized networks by stating they represent 'the vanguard of institutional innovation,' and jumps to the conclusion that they will fail to foster trust. To make this jump, the author must assume that being the vanguard of institutional innovation guarantees heavy reliance on algorithms. The correct choice provides this exact formal link via the phrasing 'No institution representing the vanguard... avoids heavy reliance,' which translates logically to: Vanguard -> Algorithmic Reliance.

Step-by-Step Solution

1
Map the conditional logic of the premises.
Foster Trust -> Transparent Governance, and Algorithmic Reliance -> ~Transparent Governance.
This establishes the core deductive chain of the argument.
2
Combine the premises to form a deduction.
Algorithmic Reliance -> ~Foster Trust.
By linking the two conditional statements, we see that relying on algorithms guarantees a failure to foster trust.
3
Identify the remaining premise and the conclusion to find the logical gap.
Premise: Decentralized Networks -> Vanguard of Innovation. Conclusion: Decentralized Networks -> ~Foster Trust. Gap: Vanguard of Innovation -> Algorithmic Reliance.
The conclusion introduces 'modern decentralized financial networks' through their descriptive trait ('vanguard of institutional innovation'). To reach the conclusion, this trait must trigger the established deduction.
4
Select the option that provides the missing conditional link.
The correct choice states that no institution in the vanguard avoids algorithmic reliance, which translates to: Vanguard -> Algorithmic Reliance.
When added to the premises, this strictly guarantees the conclusion.

Key Concept

Bridging conditional logic gaps using intermediate descriptive terms.
Estimated Time:2m 0s
Question 35Question →

Analyze each of the following logical arguments regarding a proposed city library project. Match each argument with the sufficient assumption that logically guarantees its conclusion.

Click a left item, then click its matching right item

Items

The new library will be constructed only if the federal grant is approved. The federal grant has just been approved. Thus, construction on the new library will undoubtedly begin.
If the city council approves the rezoning, the new library will be constructed. The mayor has expressed her full support for the project. Therefore, the new library will be constructed.
Constructing the new library will revitalize the downtown area. As a direct result, the city's overall tax revenue will experience a significant increase.
Unless the old community center is demolished, the new library cannot be constructed. The historical society has successfully blocked the demolition. Therefore, the federal grant will surely be revoked.

Matches

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Answer

Argument 1 matches with 'Approval of the federal grant is all that is required...'; Argument 2 matches with 'The mayor's endorsement of the project guarantees...'; Argument 3 matches with 'Any revitalization of the downtown area inevitably leads...'; Argument 4 matches with 'Failing to construct the new library guarantees...'
Each argument contains a specific logical gap that must be closed for its conclusion to be strictly justified. The correct pairs provide the exact conditional bridge (A -> B) needed to connect the disjointed premises to their respective conclusions.

Step-by-Step Solution

1
Analyze the first argument for its logical gap.
Premise: Construction requires Grant Approval. Fact: Grant Approved. Conclusion: Construction. Gap: Assumes Grant Approval guarantees Construction.
Identifying the formal logic structure reveals an illegal reversal, requiring an assumption that makes the necessary condition sufficient.
2
Analyze the second argument for its logical gap.
Premise: Rezoning guarantees Construction. Fact: Mayor Supports. Conclusion: Construction. Gap: Mayor Supports must guarantee Rezoning.
The conclusion relies on a conditional statement being triggered, requiring a link between the new evidence (mayor's support) and the trigger (rezoning).
3
Analyze the third argument for its logical gap.
Premise: Construction guarantees Revitalization. Conclusion: Construction guarantees Tax Increase. Gap: Revitalization must guarantee Tax Increase.
The conclusion introduces 'tax revenue', a new concept not found in the premises, which must be logically linked to the intermediate result.
4
Analyze the fourth argument for its logical gap.
Premise: Construction requires Demolition. Fact: No Demolition. Intermediate: No Construction. Conclusion: Grant Revoked. Gap: No Construction must guarantee Grant Revoked.
The contrapositive establishes the library won't be built. A bridge is needed to connect this established fact to the totally new consequence (grant revoked).

Key Concept

Identifying Sufficient Assumptions
Question 36Question →

Urban planner: A public transit initiative successfully reduces citywide traffic congestion only if its total end-to-end commute time is strictly less than the equivalent journey by private automobile. The proposed underground maglev system will feature longer passenger wait times at terminals than the city's current express bus network. Consequently, the proposed maglev system will fail to alleviate citywide traffic congestion.

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

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Answer: Any transit system with longer terminal wait times than the city's express bus network has a total end-to-end commute time that is at least as long as an equivalent journey by private automobile.

Answer

The assumption that any transit system with longer terminal wait times than the express bus network has a commute time at least as long as an automobile journey.
To prove the maglev will fail to alleviate congestion, we must show it fails the necessary condition provided in the first sentence (meaning its commute time must NOT be strictly less than an automobile journey). Since the only evidence given about the maglev is that its wait times are longer than the express bus network, the correct assumption must mathematically link this specific evidence to the failure of the necessary condition. The correct choice does exactly this: Wait time > Bus -> Commute Time >= Automobile. This triggers the contrapositive and guarantees the conclusion.

Step-by-Step Solution

1
Deconstruct the first premise into formal conditional logic.
Reduce Congestion -> Commute Time < Automobile.
Identifying the 'only if' condition establishes the necessary requirement for success.
2
Determine the contrapositive of the first premise, which is what the conclusion relies upon.
If Commute Time is NOT < Automobile (i.e., it is >= Automobile) -> WILL NOT Reduce Congestion.
The argument concludes that the maglev will fail to reduce congestion, so we must trigger this contrapositive.
3
Identify the remaining premise and the logical gap.
Premise given: Maglev Wait Time > Bus Wait Time. Gap: We must logically link 'Maglev Wait Time > Bus Wait Time' to 'Commute Time >= Automobile'.
A sufficient assumption must perfectly bridge the new evidence in the premises to the required trigger for the conclusion.
4
Evaluate the options to find the one that explicitly provides this conditional bridge.
The correct option states: Wait Time > Bus Wait Time -> Commute Time >= Automobile.
This provides 100% logical closure, forcing the conclusion to be true.

Key Concept

Identifying Sufficient Assumptions (Contrapositive Bridging)
Question 37Question →

A legal analyst argues: 'To secure a commercial zoning permit, a property developer must submit an environmental impact report. Any developer who submits an environmental impact report will face a mandatory public hearing. Therefore, if a property developer secures a commercial zoning permit, they must hire legal representation.'

Arrange the following logical steps in the correct sequence to construct a valid deductive chain that proves the analyst's conclusion. Your sequence must start with the initial trigger condition, proceed through the explicit premises, insert the required sufficient assumption to bridge the logical gap, and end with the final guaranteed outcome.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence builds the conditional chain logically: Permit -> Report -> Hearing -> Assumption (Hearing means Legal Rep) -> Legal Rep.
The argument's premises establish that securing a permit requires an environmental report (A -> B), and the report requires a public hearing (B -> C). The conclusion states that securing a permit requires hiring legal representation (A -> D). To validly derive this conclusion, we must bridge the gap between the end of the premise chain (C) and the conclusion's final requirement (D). The correct order mathematically reflects this logical flow: Trigger (A) -> Premise 1 (B) -> Premise 2 (C) -> Sufficient Assumption (C -> D) -> Conclusion (D).

Step-by-Step Solution

1
Identify the initial condition of the argument's conclusion.
The chain begins with 'A property developer secures a commercial zoning permit.'
Deductive chains testing conditional logic typically start with the sufficient condition of the conclusion being proven.
2
Apply the first explicit premise.
The next step is 'The developer submits an environmental impact report.'
The first premise explicitly states that securing a permit requires the submission of this report.
3
Apply the second explicit premise.
The sequence moves to 'The developer faces a mandatory public hearing.'
The second premise logically connects the submission of the report to facing a mandatory hearing.
4
Identify and insert the unstated sufficient assumption.
The assumption 'Any developer who faces a mandatory public hearing must hire legal representation' is placed next.
There is a logical gap between facing a hearing and the conclusion's requirement. This assumption logically bridges that specific gap.
5
State the final derived conclusion.
The chain ends with 'The developer must hire legal representation.'
This represents the logical closure of the argument, completing the 'then' clause of the analyst's conclusion.

Key Concept

Identifying Sufficient Assumptions in Deductive Chains
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