Examkin

Sufficient Assumption

42 questions

All types42Multiple choice21Matching11Fill in the blank10
Question 1Question →

For each reasoning sample below, identify the missing premise that is logically sufficient to prove the conclusion. Match each argument with the assumption that fully validates its inference.

Click a left item, then click its matching right item

Items

Argument 1: All benthic organisms inhabiting hadal hydrothermal trenches encounter hydrostatic pressures exceeding 60 megapascals. Hence, hadal trench organisms must synthesize specialized structural piezolytes.
Argument 2: The binding medium identified in the illuminated manuscript contains cold-pressed walnut oil. Therefore, the manuscript could not have been produced in northwestern Europe prior to 1420.
Argument 3: Central Bank Zeta adopted an explicit nominal GDP level target. Thus, market expectations of long-term real output stability in Zeta's economy will necessarily strengthen.
Argument 4: The undeciphered script on the Bronze Age clay tablets exhibits a fixed inventory of 65 discrete graphemic characters. Consequently, the script represents an open-syllable writing system rather than a morphosyllabic one.

Matches

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Answer

Argument 1 matches the premise regarding hydrostatic pressures over 60 megapascals; Argument 2 matches the universal historical exclusion regarding cold-pressed walnut oil; Argument 3 matches the unconditional linkage from nominal GDP level targeting to strengthened market expectations; Argument 4 matches the structural rule regarding scripts with exactly 65 discrete characters.
Each matched statement supplies a universal conditional rule that directly links the subject's established characteristic to the property claimed in the conclusion, leaving no logical ambiguity or gap.

Step-by-Step Solution

1
Isolate the premise and conclusion of each argument to identify the unstated conceptual leap.
Each argument introduces a new term in its conclusion (piezolyte synthesis, pre-1420 European exclusion, strengthened output expectations, open-syllable classification) that does not appear in the stated premise.
A sufficient assumption must provide a deductive bridge from the explicit premise to the new concept in the conclusion.
2
Formulate a conditional bridge statement of the form [Stated Premise Feature] →\rightarrow [Conclusion Property] for each case.
Identified the four corresponding universal conditional claims.
Assuming P→CP \rightarrow C alongside premise PP guarantees conclusion CC via Modus Ponens.
3
Pair each argument with its exact formal bridge and verify logical sufficiency.
All four arguments form deductively airtight syllogisms with zero remaining inferential gap.
Sufficient assumptions must 100% validate the argument without requiring secondary support.

Key Concept

Sufficient Assumption and Deductive Conditional Bridging
Estimated Time:2m 0s
Question 2Question →

Astrophysicist: Any star cluster that formed in an environment with high stellar density underwent rapid gravitational relaxation during its infancy. Star clusters that undergo rapid gravitational relaxation inevitably expel all of their intermediate-mass black holes through stellar dynamical interactions. The Pyxis cluster currently contains several intermediate-mass black holes. Therefore, the Pyxis cluster must have originated in a region with abundant molecular gas clouds.

The astrophysicist's conclusion follows logically if which one of the following is assumed?

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Answer: Any star cluster that did not originate in a region with abundant molecular gas clouds formed in an environment with high stellar density.

Answer

The assumption that any star cluster that did not originate in a region with abundant molecular gas clouds formed in an environment with high stellar density.
The credited response establishes the conditional rule that not originating in abundant molecular gas clouds implies forming in high stellar density (¬M→H\neg M \rightarrow H). The contrapositive of this statement is that not forming in high stellar density guarantees originating in abundant molecular gas clouds (¬H→M\neg H \rightarrow M). Because the premises prove that the Pyxis cluster did not form in high stellar density (¬H\neg H), this rule rigorously guarantees that Pyxis must have originated in a region with abundant molecular gas clouds.

Step-by-Step Solution

1
Analyze and diagram the formal conditional relationships in the premises.
Premise 1: Formed in high stellar density →\rightarrow Rapid gravitational relaxation (H→RH \rightarrow R). Premise 2: Rapid gravitational relaxation →\rightarrow Expel all intermediate-mass black holes (R→No BR \rightarrow \text{No } B). Combining these yields H→R→No BH \rightarrow R \rightarrow \text{No } B, with the contrapositive being: Contains intermediate-mass black holes →\rightarrow Did not undergo rapid gravitational relaxation →\rightarrow Did not form in high stellar density (B→¬R→¬HB \rightarrow \neg R \rightarrow \neg H).
Deconstructing the conditional chain isolates what is already proven from what remains unproven.
2
Evaluate the specific evidence given about the subject and identify the inferential gap.
The Pyxis cluster contains intermediate-mass black holes (BPyxisB_{\text{Pyxis}}), which deductively proves that Pyxis did not form in high stellar density (¬HPyxis\neg H_{\text{Pyxis}}). The conclusion claims that Pyxis originated in a region with abundant molecular gas clouds (MPyxisM_{\text{Pyxis}}). The deductive gap is between ¬HPyxis\neg H_{\text{Pyxis}} and MPyxisM_{\text{Pyxis}}.
A sufficient assumption must provide a conditional rule where the proven fact (¬H\neg H) guarantees the final conclusion (MM).
3
Identify the missing sufficient bridge condition.
We need the rule ¬H→M\neg H \rightarrow M, which is logically equivalent to its contrapositive ¬M→H\neg M \rightarrow H ('If a star cluster did not originate in abundant molecular gas clouds, it formed in high stellar density').
Adding ¬H→M\neg H \rightarrow M to the premise deduction ¬HPyxis\neg H_{\text{Pyxis}} 100% logically forces the conclusion MPyxisM_{\text{Pyxis}}.

Key Concept

Sufficient Assumption / Conditional Contrapositive Chain
Estimated Time:2m 0s
Question 3Question →

Each of the following arguments contains an inferential gap between its premises and its conclusion. Match each incomplete argument on the left with the assumption on the right that, if added as an additional premise, is logically sufficient to make the argument's conclusion follow with absolute deductive certainty.

Click a left item, then click its matching right item

Items

Argument 1: Any neural architecture that operates strictly via predictive coding generates sensory predictions prior to receiving peripheral input. Architecture Gamma operates strictly via predictive coding. Therefore, Architecture Gamma cannot produce unmediated representations of external reality.
Argument 2: Any jurisdiction that eliminates statutory damages for trade secret misappropriation experiences a decrease in proprietary patent filings. Jurisdiction Delta has not experienced a decrease in proprietary patent filings. Hence, Jurisdiction Delta has maintained high levels of domestic research and development expenditure.
Argument 3: No oceanic ecosystem subject to severe ocean acidification maintains baseline calcification rates in hermatypic corals. The Pelican Reef ecosystem has maintained baseline calcification rates in hermatypic corals. Consequently, the Pelican Reef ecosystem was not exposed to anthropogenic atmospheric carbon spikes.

Matches

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Answer

Argument 1 matches with the premise that systems generating sensory predictions prior to peripheral input cannot produce unmediated representations; Argument 2 matches with the premise that jurisdictions not eliminating statutory damages maintain high domestic R&D expenditure; Argument 3 matches with the premise that ecosystems exposed to anthropogenic carbon spikes are subject to severe ocean acidification.
Each match correctly identifies the universal conditional statement that closes the deductive gap in the argument. The predictive coding argument requires a bridge from prior prediction generation to representational mediation. The patent filing argument requires a bridge from non-elimination of statutory damages to sustained research and development expenditure. The coral reef argument requires a conditional statement whose contrapositive connects the lack of severe ocean acidification to the absence of carbon spike exposure.

Step-by-Step Solution

1
Isolate the intermediate deductive facts established by the premises of each argument.
Argument 1 yields 'Architecture Gamma generates predictions prior to input'; Argument 2 yields via modus tollens 'Jurisdiction Delta has not eliminated statutory damages'; Argument 3 yields via modus tollens 'Pelican Reef is not subject to severe ocean acidification'.
Identifying the precise intermediate conclusions isolates the remaining deductive gap between the premises and the stated conclusion.
2
Formulate the conditional rule required to bridge each intermediate fact to its target conclusion.
For Argument 1, a rule linking 'generates predictions prior to input' to 'cannot produce unmediated representations' is required. For Argument 2, a rule linking '~eliminates statutory damages' to 'maintains high R&D' is required. For Argument 3, a conditional statement whose contrapositive links '~severe ocean acidification' to '~exposed to carbon spikes' is required.
A sufficient assumption must form an unbroken formal conditional chain that guarantees the conclusion without logical defect.
3
Match each argument with its corresponding universal conditional bridge.
Argument 1 pairs with the unmediated representation rule; Argument 2 pairs with the statutory damages to R&D rule; Argument 3 pairs with the carbon spikes to acidification rule.
Each selected assumption supplies 100% deductive sufficiency.

Key Concept

Sufficient Assumption in Formal Conditional Logic
Estimated Time:2m 30s
Question 4Question →

Match each incomplete logical argument with the missing bridge premise that, if assumed, logically guarantees the truth of its conclusion.

Click a left item, then click its matching right item

Items

Glaciology Argument:
Premise: Every polar ice core segment exhibiting elevated methanesulfonic acid concentration was deposited during an epoch of expanded sea ice cover.
Conclusion: Therefore, Core Sample V-9V\text{-}9 was deposited during a period of sustained marine phytoplankton proliferation.
Admiralty Jurisprudence Argument:
Premise: No maritime vessel seized outside territorial waters is subject to domestic prize court jurisdiction unless the seizing state maintained an active naval blockade at the time of interdiction.
Conclusion: Therefore, the merchant vessel Aurelia is not subject to domestic prize court jurisdiction.
Mantle Petrology Argument:
Premise: Any mantle xenolith containing coesite inclusions underwent ultrahigh-pressure metamorphism exceeding three gigapascals.
Conclusion: Therefore, Rock Specimen X-42X\text{-}42 originated at a subduction depth greater than ninety kilometers.

Matches

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Answer

Glaciology Argument pairs with the premise supplying Core Sample V-9V\text{-}9's elevated methanesulfonic acid concentration and linking expanded sea ice cover to phytoplankton proliferation; Admiralty Jurisprudence Argument pairs with the premise establishing that the merchant vessel Aurelia was seized outside territorial waters without an active blockade; Mantle Petrology Argument pairs with the premise establishing Rock Specimen X-42X\text{-}42's coesite content and linking pressures over three gigapascals to depths over ninety kilometers.
Each matched premise provides the exact missing factual instantiation and conditional link needed to form an unbroken deductive syllogism (Premise + Assumption ⇒\Rightarrow Conclusion).

Step-by-Step Solution

1
Isolate the inferential gap in the glaciology argument
Identified that Core Sample V-9V\text{-}9 must possess the initial condition (elevated methanesulfonic acid) and that expanded sea ice must guarantee phytoplankton proliferation.
Sufficient assumptions must close all conditional leaps from premises to conclusion.
2
Isolate the inferential gap in the admiralty jurisprudence argument
Recognized the conditional rule: jurisdiction requires territorial waters OR an active naval blockade; the contrapositive requires outside waters AND no active blockade to reach no jurisdiction.
The conclusion claims non-jurisdiction, which requires satisfying both negated necessary conditions.
3
Isolate the inferential gap in the mantle petrology argument
Linked the initial premise condition (coesite inclusions) to the intermediate stage (>3 GPa>3\text{ GPa}) and bridged that to the conclusion (>90 km>90\text{ km}).
A complete deductive chain requires instantiation of the subject and a universal conditional bridge from intermediate to final property.

Key Concept

Sufficient Assumption deductive bridge completion
Estimated Time:1m 30s
Question 5Question →

Agricultural Scientist: Any commercial crop that requires continuous subsoil moisture during germination will suffer widespread yield failure when planted in arid regions lacking automated irrigation infrastructure. Field trials demonstrate that the newly bred sorghum variety S-29 does not suffer widespread yield failure when planted in arid regions lacking automated irrigation infrastructure. Thus, sorghum variety S-29 is well suited for cultivation by dryland subsistence farmers.

The agricultural scientist's conclusion follows logically if which one of the following is assumed?

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Answer: Any commercial crop that does not require continuous subsoil moisture during germination is well suited for cultivation by dryland subsistence farmers.

Answer

Any commercial crop that does not require continuous subsoil moisture during germination is well suited for cultivation by dryland subsistence farmers.
The argument provides a conditional premise: requiring continuous subsoil moisture leads to widespread yield failure in non-irrigated arid regions. Since sorghum variety S-29 does not suffer widespread yield failure in these regions, the contrapositive establishes that variety S-29 does not require continuous subsoil moisture during germination. The correct answer provides the exact universal premise needed to complete the syllogism: if any crop that does not require continuous subsoil moisture is well suited for cultivation by dryland subsistence farmers, then sorghum variety S-29 must be well suited for cultivation by those farmers.

Step-by-Step Solution

1
Analyze the premises and identify any intermediate deductive inferences.
Premise 1 states that requiring continuous subsoil moisture during germination guarantees widespread yield failure in non-irrigated arid regions. Premise 2 states that sorghum variety S-29 does not suffer widespread yield failure in non-irrigated arid regions. By contrapositive, sorghum variety S-29 does not require continuous subsoil moisture during germination.
Deconstructing the formal logic reveals what has already been proven versus what remains unproven.
2
Identify the logical gap between the intermediate deduction and the conclusion.
The intermediate deduction establishes that sorghum variety S-29 lacks the requirement for continuous subsoil moisture, but the conclusion claims it is well suited for cultivation by dryland subsistence farmers.
A sufficient assumption must provide a 100% airtight bridge linking the established trait to the new term in the conclusion.
3
Evaluate the answer choices for a sufficient conditional bridge.
The statement specifying that any commercial crop not requiring continuous subsoil moisture during germination is well suited for cultivation by dryland subsistence farmers connects the intermediate fact directly to the conclusion.
Connecting 'no requirement for continuous subsoil moisture' to 'well suited for cultivation by dryland subsistence farmers' deductively guarantees the conclusion.

Key Concept

Sufficient Assumption Deductive Linkage
Estimated Time:1m 15s
Question 6Question →

Ethicist: Any corporate governance mechanism that fails to hold executive officers individually accountable for systemic negligence inevitably undermines fiduciary transparency. Furthermore, an institution cannot maintain long-term investor trust unless it upholds fiduciary transparency. Because the recently implemented Auditing Reform Framework does not establish clear statutory liability for executive oversight committees, this framework will fail to maintain long-term investor trust.

The ethicist's conclusion follows logically if which one of the following is assumed?

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Answer: A corporate governance mechanism fails to hold executive officers individually accountable for systemic negligence if it does not establish clear statutory liability for executive oversight committees.

Answer

A corporate governance mechanism fails to hold executive officers individually accountable for systemic negligence if it does not establish clear statutory liability for executive oversight committees.
The correct answer provides the exact missing premise required to make the argument deductively valid. Combining the premise that the framework lacks clear statutory liability with the conditional rule that lacking clear statutory liability implies failing to hold officers individually accountable triggers the entire logical sequence: Lacks Statutory Liability → Fails Accountability → Undermines Transparency → Fails to Maintain Trust.

Step-by-Step Solution

1
Analyze and diagram the stated conditional premises and conclusion.
Premise 1: Fails Individual Accountability → Undermines Fiduciary Transparency. Premise 2: Maintains Trust → Upholds Fiduciary Transparency (Contrapositive: Undermines Fiduciary Transparency → Fails to Maintain Trust). Fact: Auditing Reform Framework lacks clear statutory liability for executive oversight committees. Conclusion: Auditing Reform Framework will fail to maintain long-term investor trust.
Deconstructing the argument into formal logic reveals the exact chain: Fails Individual Accountability → Undermines Transparency → Fails to Maintain Trust.
2
Identify the inferential gap between the factual premise and the conditional chain.
The premises connect 'Fails Individual Accountability' to 'Fails to Maintain Trust', but the stimulus introduces a new concept in the premise: 'lacks clear statutory liability for executive oversight committees'.
A sufficient assumption must bridge the new term in the premise (lacking statutory liability) to the trigger of the conditional chain (failing individual accountability).
3
Evaluate the answer choices to identify the statement that deductively guarantees the conclusion.
The statement specifying that lacking clear statutory liability guarantees a failure of individual accountability creates the unbroken chain: Lacks Statutory Liability → Fails Individual Accountability → Undermines Transparency → Fails Trust.
This 100% closes the deductive gap, making the conclusion follow necessarily from the premises.

Key Concept

Sufficient Assumption in Multi-Step Conditional Reasoning
Estimated Time:2m 0s
Question 7Question →

Complete the legal theorist's formal argument by filling in the blank with the precise condition that logically guarantees the argument's conclusion.

Fill in the blanks below

Premise 1: Any sovereign trade agreement that lacks binding multilateral enforcement mechanisms is incapable of deterring state-sponsored cyberespionage.
Premise 2: Any regulatory framework that fails to protect critical national infrastructure.
Premise 3: The Proposed Trans-Pacific Cyber Accord is a sovereign trade agreement that lacks binding multilateral enforcement mechanisms.
Conclusion: Therefore, the Proposed Trans-Pacific Cyber Accord fails to protect critical national infrastructure.
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Answer

is incapable of deterring state-sponsored cyberespionage
Premise 1 and Premise 3 together prove deductively that the Proposed Trans-Pacific Cyber Accord is incapable of deterring state-sponsored cyberespionage. For the conclusion ('The Accord fails to protect critical national infrastructure') to follow with absolute certainty, Premise 2 must establish a universal rule dictating that any framework that is incapable of deterring state-sponsored cyberespionage inevitably fails to protect critical national infrastructure. Inserting 'is incapable of deterring state-sponsored cyberespionage' completes the valid transitive chain (A→B→C→D)(A \rightarrow B \rightarrow C \rightarrow D).

Step-by-Step Solution

1
Isolate the established premises and the target conclusion
Premise 3 and Premise 1 establish that the Proposed Trans-Pacific Cyber Accord belongs to the category of agreements that are incapable of deterring state-sponsored cyberespionage. The conclusion asserts that the Accord fails to protect critical national infrastructure.
Deconstructing the argument into formal conditional terms reveals the starting subject and the final deduced attribute.
2
Map the inferential gap between the intermediate predicate and the conclusion
We have the chain: [Trans-Pacific Accord] →\rightarrow [Lacks binding enforcement] →\rightarrow [Incapable of deterring cyberespionage]. The conclusion requires: [Trans-Pacific Accord] →\rightarrow [Fails to protect critical national infrastructure].
A sufficient assumption must provide a 100% deductive bridge linking the intermediate property to the final predicate.
3
Formulate the missing universal conditional statement
Premise 2 must state that [Incapable of deterring cyberespionage] →\rightarrow [Fails to protect critical national infrastructure]. Therefore, the blank must be filled with 'is incapable of deterring state-sponsored cyberespionage'.
Supplying this specific antecedent completes the unbroken conditional chain: [Accord] →\rightarrow [Incapable of deterring cyberespionage] →\rightarrow [Fails to protect infrastructure].

Key Concept

Sufficient Conditional Bridging in Formal Syllogisms
Estimated Time:1m 30s
Question 8Question →

Paleoanthropologist: Any technological practice that requires the multi-stage thermal alteration of mineral raw materials demonstrates that its practitioners possessed working-memory capacity equivalent to that of modern humans. In the Middle Stone Age, the fabrication of silcrete micro-blades invariably required multi-stage thermal alteration. Recent excavations at the southern coastal site of Pinnacle Point have uncovered an abundance of complex composite tools bound by organic adhesives. Therefore, the Middle Stone Age inhabitants of Pinnacle Point possessed working-memory capacity equivalent to that of modern humans.

The paleoanthropologist's conclusion follows logically if which one of the following is assumed?

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Answer: All composite tools bound by organic adhesives that were produced at Pinnacle Point incorporated silcrete micro-blades.

Answer

The statement that all composite tools bound by organic adhesives produced at Pinnacle Point incorporated silcrete micro-blades logically guarantees the conclusion.
The conclusion claims that the inhabitants of Pinnacle Point possessed modern working-memory capacity. The premises establish that fabricating silcrete micro-blades guarantees multi-stage thermal alteration, which in turn guarantees modern working memory. The archaeological evidence at Pinnacle Point only establishes the presence of composite tools bound by organic adhesives. Assuming that all such composite tools produced at Pinnacle Point incorporated silcrete micro-blades connects the physical evidence to the beginning of the deductive chain, proving the conclusion with 100% certainty.

Step-by-Step Solution

1
Deconstruct the argument into formal premises and identify the conclusion.
Premise 1: Multi-stage thermal alteration of minerals implies working-memory equivalent to modern humans. Premise 2: Fabricating silcrete micro-blades implies multi-stage thermal alteration. Premise 3: Inhabitants of Pinnacle Point produced composite tools bound by organic adhesives. Conclusion: Inhabitants of Pinnacle Point possessed working-memory equivalent to modern humans.
Sufficient assumption questions require identifying the exact gap in the deductive chain.
2
Determine the conditional chain established by the premises.
Fabrication of silcrete micro-blades leads to multi-stage thermal alteration, which in turn proves modern working-memory capacity.
Combining the first two conditional premises establishes the pathway to the conclusion.
3
Identify the unlinked term in the evidence and bridge it to the conditional chain.
The evidence only mentions composite tools bound by organic adhesives. To reach the conclusion, this evidence must guarantee the starting point of the chain: the fabrication of silcrete micro-blades.
Connecting adhesive-bound composite tools directly to silcrete micro-blades deductively forces the conclusion to follow.

Key Concept

Sufficient Assumption Deductive Bridging
Estimated Time:1m 45s
Question 9Question →

Political Theorist: For any grassroots insurgency to achieve systemic political reform, it must maintain ideological orthodoxy while simultaneously cultivating a broad electoral consensus. Cultivating such a consensus universally necessitates that the insurgency's leadership forge alliances with incumbent political factions. Yet, the very act of forging alliances with incumbent political factions inevitably compromises the foundational tenets of the insurgency's original manifesto. It therefore follows that no grassroots insurgency can achieve systemic political reform.

The conclusion of the political theorist's argument follows logically if which one of the following is assumed?

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Answer: A grassroots insurgency maintains ideological orthodoxy only if it does not compromise the foundational tenets of its original manifesto.

Answer

The option stating that an insurgency maintains ideological orthodoxy only if it does not compromise the foundational tenets of its original manifesto.
The argument relies on formal logic. Let's map it: Achieving systemic reform (A) requires both maintaining ideological orthodoxy (B) and cultivating a broad consensus (C). So, A requires B and C. The theorist then states that cultivating consensus (C) requires forging alliances (D), which in turn inevitably compromises foundational tenets (E). By chaining these premises, we deduce that if an insurgency achieves reform (A), it must maintain orthodoxy (B) AND compromise its tenets (E). However, the conclusion jumps to the absolute claim that achieving reform is impossible. To prove this conclusion, we must introduce a rule that makes it impossible to simultaneously do both B and E. The credited response provides exactly this rule: 'maintaining orthodoxy' (B) requires 'NOT compromising tenets' (NOT E). If we assume B -> NOT E, then achieving reform (A) would require an insurgency to both compromise (E) and not compromise (NOT E), which is a logical contradiction. Thus, reform (A) is impossible, perfectly justifying the conclusion.

Step-by-Step Solution

1
Map the formal logic of the argument's premises and conclusion.
Conclusion: Reform -> Impossible. Premises: Reform -> (Orthodoxy AND Consensus). Consensus -> Alliances. Alliances -> Compromise.
Understanding the chain of conditional statements is required to find the deductive gap.
2
Trace the causal/conditional chain created by the premises.
Reform -> Consensus -> Alliances -> Compromise. Therefore, achieving Reform guarantees that the insurgency Compromises.
Consolidating the premises reveals what must logically follow if the sufficient condition (Reform) is met.
3
Identify the deductive gap between the premise chain and the conclusion.
The premises prove that Reform -> (Orthodoxy AND Compromise). The conclusion claims Reform is impossible. The missing link must establish that Orthodoxy and Compromise are mutually exclusive.
For the conclusion to be 100% valid, the assumption must force a logical contradiction when Reform is achieved.
4
Formulate the sufficient assumption to bridge the gap.
If an insurgency maintains Orthodoxy, it cannot Compromise (Orthodoxy -> NOT Compromise). If we add this assumption, achieving Reform requires an insurgency to both Compromise and NOT Compromise, a contradiction that proves Reform is impossible.
This specific conditional relationship guarantees the argument's absolute conclusion.

Key Concept

Identifying the missing deductive link (sufficient assumption) in a formal logic chain by mapping conditional statements.
Estimated Time:2m 0s
Question 10Question →

Analyze the cognitive scientist's argument below. To make the conclusion logically valid, you must supply the missing conditional premise. Fill in the blanks using the exact terminology from the argument to construct the precise sufficient assumption.

Fill in the blanks below

Cognitive Scientist: A computational system possesses genuine semantic understanding only if it can ground its internal symbols in sensorimotor interactions with a physical environment. Because large language models are trained purely by mapping statistical relationships between text tokens, they completely lack sensorimotor engagement with the physical world. Therefore, it is clear that any system incapable of causal reasoning cannot possess genuine semantic understanding.

Missing Premise: A computational system is able to ground its internal in sensorimotor interactions only if it is capable of .
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Answer

symbols, causal, reasoning
The correct answer successfully bridges the strict logical gap between the first premise and the conclusion while avoiding the decoy premise about large language models. The argument's core premise is GSU -> G (Genuine Semantic Understanding requires Grounding symbols). The conclusion asserts ~CR -> ~GSU (Lack of Causal Reasoning guarantees lack of Genuine Semantic Understanding). To validate this conclusion, we must establish that ~CR guarantees ~G. The contrapositive of this required assumption is G -> CR (Grounding symbols requires Causal Reasoning). The fill-in-the-blank sentence is structured as 'G only if CR', exactly mirroring this required sufficient assumption. Using the exact text terms yields 'symbols', 'causal', and 'reasoning'.

Step-by-Step Solution

1
Map the formal logic of the core premise.
Genuine Semantic Understanding (GSU) -> Grounds symbols in sensorimotor interactions (G).
The phrase 'only if' introduces a necessary condition.
2
Map the formal logic of the conclusion.
No Causal Reasoning (~CR) -> No Genuine Semantic Understanding (~GSU).
This is the final claim the argument attempts to prove.
3
Identify and isolate the decoy premise.
Large Language Model (LLM) -> No sensorimotor engagement (~G).
This premise shares a term (~G) with the main conditional chain but introduces a specific subject (LLMs) that does not appear in the generalized conclusion.
4
Determine the required deductive gap.
We must prove ~CR -> ~GSU. We know from Step 1 that ~G -> ~GSU (contrapositive). Therefore, we need an assumption establishing that ~CR -> ~G.
Linking the dangling term in the conclusion (~CR) to the necessary condition of the first premise (~G) forms a valid chain: ~CR -> ~G -> ~GSU.
5
Contrapose the required assumption to match the fill-in-the-blank structure.
The assumption ~CR -> ~G is logically equivalent to G -> CR (Grounding symbols requires Causal Reasoning).
The provided sentence template 'A system is able to ground its internal... only if it is capable of...' represents the G -> CR structure.

Key Concept

Formal deduction involving contrapositives and the circumvention of decoy premises in conditional logic chains.
Estimated Time:2m 30s
Question 11Question →

Read the argument and complete the missing premise that makes the conclusion follow logically with absolute deductive certainty.

Fill in the blanks below

Biochemist: Any metabolic enzyme that requires zinc cofactor binding is structurally destabilized at temperatures exceeding 45°C. The newly isolated bacterial protease P-329 remains structurally stable at 50°C. Therefore, P-329 cannot catalyze peptide bond hydrolysis under physiological conditions.

The biochemist's conclusion follows logically if it is assumed that any metabolic enzyme that catalyzes peptide bond hydrolysis under physiological conditions .
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Answer

requires zinc cofactor binding
The premises establish that protease P-329 remains stable at 50°C, which by contrapositive of the first premise proves that P-329 does not require zinc cofactor binding. The conclusion asserts that P-329 cannot catalyze peptide bond hydrolysis under physiological conditions. For this conclusion to follow necessarily, lacking zinc cofactor binding must be sufficient to prevent catalytic activity, meaning that requiring zinc cofactor binding is a necessary requirement for catalysis. Therefore, assuming that any enzyme that catalyzes peptide bond hydrolysis requires zinc cofactor binding enables the valid deductive inference: Catalyzes Hydrolysis -> Requires Zinc -> Destabilized >45°C. Since P-329 is stable at 50°C, it cannot require zinc, and thus cannot catalyze hydrolysis.

Step-by-Step Solution

1
Analyze and diagram the explicit premises given in the stimulus.
Premise 1: Requires zinc cofactor binding -> Destabilized above 45°C. Contrapositive: Stable at or above 45°C -> Does not require zinc cofactor binding. Premise 2: P-329 is stable at 50°C. Combining these yields the intermediate deduction: P-329 does not require zinc cofactor binding.
Establishing what is strictly proven by the premises reveals the exact starting point of the inferential gap.
2
Identify the conclusion and isolate the logical gap.
Conclusion: P-329 cannot catalyze peptide bond hydrolysis under physiological conditions. The intermediate deduction establishes that P-329 lacks zinc cofactor binding, but the argument concludes that P-329 lacks the ability to catalyze peptide bond hydrolysis.
A sufficient assumption must provide a universal bridge connecting the established condition (does not require zinc cofactor binding) to the final conclusion (cannot catalyze peptide bond hydrolysis).
3
Construct the missing bridge premise in the required conditional format.
To deduce that lacking zinc cofactor binding guarantees inability to catalyze hydrolysis, we need: No zinc cofactor binding -> Cannot catalyze hydrolysis. The contrapositive of this bridge is: Catalyzes peptide bond hydrolysis -> Requires zinc cofactor binding.
The stem frames the assumption starting with 'any metabolic enzyme that catalyzes peptide bond hydrolysis under physiological conditions...', requiring the completion 'requires zinc cofactor binding' to complete the valid chain.

Key Concept

Sufficient Assumption Deductive Bridging
Question 12Question →

Match each incomplete deductive argument with the corresponding bridge assumption that, if assumed, enables the argument's conclusion to follow logically from its premises.

Click a left item, then click its matching right item

Items

Argument 1 (Paleoceanography):
Premise: Core samples from the Weddell Sea contain elevated concentrations of terrigenous quartz silt deposited during the mid-Pliocene epoch.
Premise: Any sedimentary deposit containing terrigenous quartz silt in that region was transported exclusively by expanded sub-ice shelf meltwater currents.
Conclusion: Therefore, mid-Pliocene sea-surface temperatures in the Weddell Sea were at least 3∘C3^\circ\text{C} warmer than present-day levels.
Argument 2 (Epigraphy):
Premise: The Linear C inscriptions discovered at the Kourion sanctuary site contain non-repetitive numeric tally marks aligned with lunar cycle intervals.
Premise: Any archaeological text containing numeric tallies synchronized to celestial intervals served as an administrative calendar for civic harvest taxation.
Conclusion: Therefore, the Linear C inscriptions represent an official legal decree rather than personal devotional graffiti.
Argument 3 (Pharmacology):
Premise: The experimental kinase inhibitor compound ZT-409 suppresses cardiac microvascular pericyte proliferation in in-vitro human assays.
Premise: Any pharmacological compound that inhibits cardiac pericyte proliferation inevitably degrades ventricular contractile compliance in live mammalian tissue.
Conclusion: Therefore, Phase III human clinical trials for ZT-409 ought to be immediately suspended by regulatory oversight boards.

Matches

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Answer

Argument 1 matches with the assumption linking meltwater currents to temperatures at least 3∘C3^\circ\text{C} warmer; Argument 2 matches with the assumption linking administrative harvest taxation calendars to official legal decrees; Argument 3 matches with the assumption linking ventricular contractile degradation to mandatory Phase III trial suspension.
Each matched pair supplies the exact conditional premise required to make the conclusion follow inescapably from the stated premises. In Argument 1, the premise chain established meltwater currents; assuming that meltwater transport requires temperatures at least 3∘C3^\circ\text{C} warmer guarantees the temperature conclusion. In Argument 2, the premises established that the text is an administrative harvest calendar; assuming all such calendars are official legal decrees guarantees the legal decree conclusion. In Argument 3, the premises established ventricular compliance degradation; assuming that such degradation mandates immediate clinical trial suspension guarantees the regulatory suspension conclusion.

Step-by-Step Solution

1
Analyze each argument's premise chain and identify the unlinked term in its conclusion.
Found the exact inferential gaps: Argument 1 needs a link between meltwater transport and temperature rise; Argument 2 needs a link between harvest taxation calendars and official legal decrees; Argument 3 needs a link between ventricular compliance degradation and clinical trial suspension.
A sufficient assumption must bridge the gap between the existing premises and the conclusion so that the conclusion is deductively guaranteed.
2
Formulate the required conditional statement (A→BA \rightarrow B) for each scenario.
Formulated: (1) Meltwater Transport →\rightarrow Temperature ≥3∘C\ge 3^\circ\text{C} Warmer; (2) Harvest Taxation Calendar →\rightarrow Official Legal Decree; (3) Ventricular Compliance Degradation →\rightarrow Suspend Phase III Trials.
Conditional bridges ensure complete logical sufficiency without allowing counterexamples.
3
Match each argument on the left to its exact corresponding conditional bridge on the right.
Successfully paired Argument 1 with the temperature bridge, Argument 2 with the legal decree bridge, and Argument 3 with the clinical trial suspension bridge.
Each right-hand statement supplies the precise premise needed to complete the deductive syllogism of its respective left-hand argument.

Key Concept

Sufficient Assumption Identification in Deductive Syllogisms
Estimated Time:1m 30s
Question 13Question →

For each of the incomplete arguments in the left column, select the corresponding missing premise from the right column that, if assumed, logically guarantees the truth of that argument's conclusion.

Click a left item, then click its matching right item

Items

Neuroscientist: Every neural pathway that exhibits high-frequency gamma oscillations undergoes long-term potentiation. The entorhinal cortex pathways activated during novel spatial navigation undergo long-term potentiation. Therefore, the entorhinal cortex pathways activated during novel spatial navigation exhibit high-frequency gamma oscillations.
Jurisprudential Scholar: No customary maritime rule that lacks reciprocal enforcement qualifies as a valid statutory obligation. In ancient Mediterranean maritime law, the Lex Rhodia enforced shared cargo liability upon shipwreck. Therefore, the Lex Rhodia created valid statutory obligations.
Geochemist: Mineral crusts formed in deep sub-seafloor serpentinization zones are enriched with abiogenic methane. Any geochemical deposit enriched with abiogenic methane provides an energy substrate capable of sustaining anaerobic microbial ecosystems. Thus, all mineral crusts formed in deep sub-seafloor serpentinization zones preserve biosignatures of primordial metabolic activity.

Matches

Show answer & explanation

Answer

The neuroscientist's argument matches with the premise that all pathways undergoing long-term potentiation exhibit gamma oscillations; the legal scholar's argument matches with the premise that enforcing shared cargo liability qualifies as a valid statutory obligation; and the geochemist's argument matches with the premise that providing an anaerobic microbial energy substrate guarantees the preservation of primordial biosignatures.
Each matched premise bridges the explicit deductive gap in its respective argument. For the first argument, the premise stating that long-term potentiation implies gamma oscillations resolves the reversal gap. For the second argument, the premise connecting shared cargo liability to valid statutory obligation creates a direct deductive chain. For the third argument, the premise connecting microbial energy substrates to the preservation of primordial biosignatures closes the new-concept gap.

Step-by-Step Solution

1
Isolate the formal premises and conclusion for the neuroscientist's argument and identify the inferential gap.
Premise: Gamma →\rightarrow Potentiation; Premise: Navigation →\rightarrow Potentiation; Conclusion: Navigation →\rightarrow Gamma. The gap is the converse relationship: Potentiation →\rightarrow Gamma.
Sufficient assumptions must 100% bridge the gap between premise terms and conclusion terms.
2
Isolate the terms in the jurisprudential scholar's argument to find the missing conditional link.
Premise: Lex Rhodia →\rightarrow Shared liability; Conclusion: Lex Rhodia →\rightarrow Valid statutory obligation. The gap requires linking shared cargo liability directly to valid statutory obligations.
The existing premise regarding reciprocal enforcement is merely a necessary condition that does not affirmatively establish validity.
3
Isolate the chain in the geochemist's argument and identify the rogue concept in the conclusion.
Premises establish Crust →\rightarrow Methane →\rightarrow Microbial energy substrate. The conclusion introduces 'preserves primordial biosignatures'. The gap is Microbial energy substrate →\rightarrow Preserves primordial biosignatures.
A sufficient assumption must provide a universal bridge from the terminal premise concept to the new conclusion concept.

Key Concept

Sufficient Assumption Identification across Varied Deductive Gaps
Estimated Time:2m 30s
Question 14Question →

Complete the statement with the appropriate word or phrase to make the argument's conclusion follow logically.

Fill in the blanks below

Premise: Any employee who completes the advanced data analysis workshop is eligible for promotion to senior analyst.
Conclusion: Therefore, Marcus is eligible for promotion to senior analyst.

The conclusion follows logically if it is assumed that Marcus the advanced data analysis workshop.
Show answer & explanation

Answer

completed (or has completed)
The premise establishes a universal conditional relationship: completing the advanced data analysis workshop guarantees eligibility for promotion. To deductively prove that Marcus is eligible for promotion, we must establish that Marcus meets the trigger condition. Therefore, assuming that Marcus completed the workshop logically guarantees the truth of the conclusion.

Step-by-Step Solution

1
Identify the stated premise and the conclusion
Premise: Completes workshop implies eligible for promotion. Conclusion: Marcus is eligible for promotion.
Deconstructing the argument isolates the sufficient condition and the necessary outcome.
2
Identify the missing logical bridge needed to guarantee the conclusion
The argument requires establishing that Marcus satisfies the sufficient condition (completing the workshop).
Under Modus Ponens, if the conditional statement 'If P, then Q' is true, establishing P guarantees Q.
3
Fill in the blank with the required condition
Assuming Marcus 'completed' (or 'has completed') the workshop guarantees the conclusion with 100% deductive certainty.
Connecting Marcus directly to the sufficient condition closes the inferential gap completely.

Key Concept

Sufficient Assumption and Conditional Deduction
Question 15Question →

Each of the following arguments contains an inferential gap between its stated premise and its conclusion. Match each argument with the assumption that, if assumed, is logically sufficient to guarantee that the conclusion follows deductively.

Click a left item, then click its matching right item

Items

Premise: Any company that implements closed-loop water recycling reduces total factory waste.
Conclusion: Hydrolix Enterprises will experience increased long-term profitability.
Premise: Every municipality that builds protected cycling networks experiences a marked decrease in urban traffic congestion.
Conclusion: The city of Oakhaven will receive the National Clean Transit Award.
Premise: All medical research laboratories that use double-blind verification protocols eliminate reporting bias in clinical trials.
Conclusion: Vitasyn Laboratories will secure immediate regulatory authorization.

Matches

Show answer & explanation

Answer

Each argument is matched with the conditional statement linking its explicit intermediate outcome to its specific final conclusion: the Hydrolix argument pairs with the statement that reducing factory waste yields increased long-term profitability; the Oakhaven argument pairs with the statement that decreased traffic congestion earns the National Clean Transit Award; and the Vitasyn argument pairs with the statement that eliminating reporting bias secures regulatory authorization.
For each pairing, the matched assumption provides a universal conditional link where the antecedent matches the outcome from the premise and the consequent matches the exact claim made in the conclusion. When combined with the premise, this creates a valid hypothetical syllogism that deductively validates the conclusion.

Step-by-Step Solution

1
Identify the premise and conclusion structure for each argument to isolate the unstated link.
Each argument follows a linear conditional chain where Premise establishes [Condition A → Condition B], but Conclusion claims [Entity possessing Condition A → Condition C].
Sufficient assumptions must supply a valid conditional rule [Condition B → Condition C] to connect the existing premise to the novel conclusion term.
2
Match each argument's intermediate result with the corresponding right-side rule providing the exact conclusion term.
Hydrolix's reduced factory waste connects to increased profitability; Oakhaven's decreased traffic congestion connects to the Clean Transit Award; Vitasyn's elimination of reporting bias connects to regulatory authorization.
Plugging in the premise plus the sufficient bridge fully forces the conclusion to be true in each case.

Key Concept

Sufficient Assumption Conditional Bridging
Estimated Time:1m 0s
Question 16Question →

Highcrest Nature Reserve contains several designated wetland habitats. Furthermore, any nature reserve that provides nesting grounds for migratory waterfowl is eligible for regional conservation grants. Therefore, Highcrest Nature Reserve is eligible for regional conservation grants.

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

Show answer & explanation

Answer: Any nature reserve that contains designated wetland habitats provides nesting grounds for migratory waterfowl.

Answer

The statement that any nature reserve containing designated wetland habitats provides nesting grounds for migratory waterfowl logically completes the argument.
The correct answer provides the precise universal conditional bridge needed: Designated Wetlands -> Nesting Grounds. Combining this with the fact that Highcrest has designated wetlands leads to the conclusion that Highcrest provides nesting grounds, which in turn triggers the premise guaranteeing eligibility for regional conservation grants.

Step-by-Step Solution

1
Break down the premises and conclusion into conditional components
Premise 1: Highcrest contains designated wetland habitats. Premise 2: Nesting grounds for migratory waterfowl implies eligibility for regional conservation grants. Conclusion: Highcrest is eligible for regional conservation grants.
Deconstructing the argument isolates the stated facts from the ultimate claim.
2
Identify the missing link in the chain of reasoning
The premises connect Nesting Grounds to Grants, but we only know Highcrest has Wetlands. The missing link is: Designated wetland habitats guarantee nesting grounds for migratory waterfowl.
A sufficient assumption must establish a 100% deductive bridge between the rogue premise term and the sufficient condition of the rule.
3
Select the option that supplies the exact missing conditional statement
Assuming that any nature reserve containing designated wetland habitats provides nesting grounds completes the syllogism: Highcrest -> Wetland -> Nesting Grounds -> Eligible for Grants.
This guarantees the truth of the conclusion with absolute certainty.

Key Concept

Sufficient Assumption Conditional Bridging
Estimated Time:45s
Question 17Question →

Archivist: Every historical document treated with vapor phase deacidification is completely free of acidic deterioration. The recently recovered municipal charter was treated with vapor phase deacidification. Therefore, the municipal charter is suitable for permanent archival display.

The archivist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Any historical document that is completely free of acidic deterioration is suitable for permanent archival display.

Answer

The argument's conclusion is fully guaranteed if it is assumed that any historical document completely free of acidic deterioration is suitable for permanent archival display.
The correct option provides the exact missing premise needed to form a valid deductive syllogism. The premises establish that the municipal charter was treated with vapor phase deacidification, which guarantees it is completely free of acidic deterioration. Connecting 'completely free of acidic deterioration' directly to 'suitable for permanent archival display' guarantees the truth of the conclusion without exception.

Step-by-Step Solution

1
Identify the premises and the conclusion.
Premise 1: Municipal charter was treated with vapor phase deacidification. Premise 2: Treated with vapor phase deacidification implies free of acidic deterioration. Intermediate inference: Municipal charter is free of acidic deterioration. Conclusion: Municipal charter is suitable for permanent archival display.
Deconstructing the argument isolates the stated evidentiary basis from the final claim.
2
Identify the deductive gap between the premises and the conclusion.
The premises prove the charter is 'free of acidic deterioration', but the conclusion introduces the new term 'suitable for permanent archival display'.
A sufficient assumption must provide a bridge that connects the established condition to the conclusion's new predicate.
3
Formulate the required conditional link.
If a document is free of acidic deterioration, then it is suitable for permanent archival display (Free of Deterioration -> Suitable for Display).
This conditional rule completes the deductive chain: Municipal Charter -> Treated -> Free of Deterioration -> Suitable for Display.

Key Concept

Sufficient Assumption Deductive Linkage
Estimated Time:45s
Question 18Question →

For each of the incomplete arguments below, which corresponding assumption, if established, logically guarantees the truth of its conclusion? Match each argument with its sufficient deductive bridge.

Click a left item, then click its matching right item

Items

Dendrochronologist: Any ancient timber sample that exhibits micro-cellular resin saturation was harvested during an extended drought. The ceiling beams recovered from the Oakhaven manor do not contain annual ring compression patterns. Therefore, none of the Oakhaven ceiling beams exhibit micro-cellular resin saturation.
Bioethicist: Any clinical trial protocol relying on adaptive Bayesian outcome monitoring automatically adjusts dosage allocations without requiring blinded physician intervention. The Lumina trial protocol requires blinded physician intervention. Thus, the Lumina trial protocol cannot be classified as an autonomous experimental design.
Urban Planner: Whenever a municipal transit authority implements demand-responsive micro-transit fleets, it reduces municipal spending on fixed-route arterial maintenance. The city of Riverdale experienced a measurable decline in suburban commuter transit satisfaction following its transit overhaul. Hence, the Riverdale transit overhaul involved implementing demand-responsive micro-transit fleets.

Matches

Show answer & explanation

Answer

The dendrochronology argument matches the premise linking drought to ring compression patterns; the bioethics argument matches the premise requiring autonomous designs to rely on adaptive Bayesian monitoring; and the urban planning argument matches the premise stating that satisfaction declines entail demand-responsive fleet implementation.
Each paired premise bridges the exact conceptual gap in its respective argument by establishing a universal conditional relationship, making the conclusion deductively inescapable through modus ponens or modus tollens.

Step-by-Step Solution

1
Analyze the inferential gap in the dendrochronology argument.
Premises link resin saturation to drought, and note the absence of ring compression. To deduce the absence of resin saturation from the absence of ring compression, we need a conditional bridge from drought to ring compression.
Applying contrapositive logic (no ring compression -> no drought -> no resin saturation) 100% guarantees the conclusion.
2
Analyze the inferential gap in the bioethics argument.
Premises establish that the Lumina protocol does not use adaptive Bayesian monitoring. The conclusion claims Lumina is not an autonomous design.
Connecting 'autonomous design' as a sufficient condition for 'adaptive Bayesian monitoring' allows the contrapositive to deductively yield 'not an autonomous design'.
3
Analyze the inferential gap in the urban planning argument.
Premise notes a decline in suburban commuter satisfaction, and concludes Riverdale implemented demand-responsive fleets.
A sufficient assumption must state that experiencing a satisfaction decline guarantees the implementation of demand-responsive micro-transit fleets.

Key Concept

Sufficient Assumption and Conditional Deduction
Estimated Time:1m 30s
Question 19Question →

Linguist: The newly developed Babel-X translation model processes textual input without dynamically reweighting token vectors based on surrounding sentence syntax. However, any language model that fails to resolve figurative idioms cannot produce accurate translations of literary prose. Therefore, Babel-X cannot produce accurate translations of literary prose.

The linguist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Any language model that processes textual input without dynamically reweighting token vectors based on surrounding sentence syntax fails to resolve figurative idioms.

Answer

The assumption that any language model that processes textual input without dynamically reweighting token vectors based on surrounding sentence syntax fails to resolve figurative idioms.
The stimulus presents two separate premises: Babel-X lacks dynamic token reweighting based on syntax, and any system that fails to resolve figurative idioms cannot produce accurate literary translations. To deductively guarantee the conclusion that Babel-X cannot produce accurate literary translations, we must bridge Babel-X's processing characteristic to the failure of idiom resolution. The statement that any model lacking dynamic token reweighting fails to resolve figurative idioms provides this exact deductive bridge, completing the valid syllogism.

Step-by-Step Solution

1
Identify the premises and conclusion in the stimulus
Premise 1: Babel-X lacks dynamic token reweighting. Premise 2: Lacks idiom resolution implies cannot produce accurate literary translations. Conclusion: Babel-X cannot produce accurate literary translations.
Deconstructing the argument reveals the explicit terms and the missing connection.
2
Identify the inferential gap
There is no stated link between lacking dynamic token reweighting and failing to resolve figurative idioms.
A sufficient assumption must provide a 100% deductive link from the premise condition to the antecedent of the final rule.
3
Construct the missing bridge premise
Lacking dynamic token reweighting →\rightarrow Fails to resolve figurative idioms.
Adding this conditional bridge completes the chain: Babel-X →\rightarrow Lacks dynamic token reweighting →\rightarrow Fails to resolve figurative idioms →\rightarrow Cannot produce accurate literary translations.

Key Concept

Sufficient Assumption Conditional Bridging
Estimated Time:1m 15s
Question 20Question →

An archaeologist analyzes ceramic production methods across ancient regional settlements and constructs the following deductive argument. Which terms correctly fill in the blanks to complete the sufficient assumption that makes the conclusion follow with absolute logical certainty?

Fill in the blanks below

Premise 1: Any ceramic vessel containing high scandium concentrations was fired in kilns fueled exclusively by highland tamarack.
Premise 2: Any kiln fueled exclusively by highland tamarack is incapable of reaching temperatures exceeding 900 degrees Celsius.
Conclusion: Therefore, no ceramic vessel containing high scandium concentrations was produced in the lowland coastal workshops.

Sufficient Bridge: The conclusion follows logically if it is assumed that every ceramic vessel produced in the lowland coastal workshops was fired at a temperature 900 degrees Celsius, thereby precluding the use of .
Show answer & explanation

Answer

The argument requires establishing that lowland coastal workshop vessels were fired at temperatures exceeding 900 degrees Celsius, which precludes the use of highland tamarack.
The premises establish that containing high scandium concentrations requires using highland tamarack (Scandium -> Tamarack), which in turn requires firing temperatures at or below 900°C (Tamarack -> <=900°C). By contrapositive, any ceramic fired at a temperature above 900°C cannot have used highland tamarack (>900°C -> Not Tamarack) and therefore cannot contain high scandium concentrations (Not Tamarack -> Not Scandium). Assuming that every vessel produced in lowland coastal workshops was fired above 900°C (precluding highland tamarack) deductively guarantees that no lowland coastal vessel contains high scandium concentrations.

Step-by-Step Solution

1
Map the formal conditional relationships in the premises
Premise 1 yields 'Scandium implies Highland Tamarack'. Premise 2 yields 'Highland Tamarack implies Firing Temperature at most 900°C'. Combining these by transitivity yields 'Scandium implies Firing Temperature at most 900°C'.
Establishing the intermediate conditional chain is necessary to identify the scope of what scandium ceramics entail.
2
Take the contrapositive of the combined premises
Contrapositive: 'Firing Temperature exceeding 900°C implies No Highland Tamarack, which implies No Scandium'.
The conclusion claims that vessels from lowland coastal workshops contain no scandium; linking lowland workshops to a temperature above 900°C enables the contrapositive chain.
3
Identify the missing sufficient link to establish the conclusion
Assuming 'Lowland Coastal implies Firing Temperature above 900°C' guarantees that lowland ceramics could not use highland tamarack, thereby deductively guaranteeing that no lowland ceramic contains scandium.
A sufficient assumption must close the inferential gap 100% deductively: Lowland implies >900°C implies Not Highland Tamarack implies Not Scandium.

Key Concept

Sufficient Assumption via Contrapositive Conditional Linkage
Estimated Time:1m 30s
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