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Difficulty: HardSufficient Assumption

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.

  • Argument 1: All benthic organisms inhabiting hadal hydrothermal trenches encounter hydrostatic pressures exceeding 60 megapascals. Hence, hadal trench organisms must synthesize specialized structural piezolytes.Any organism that encounters hydrostatic pressures exceeding 60 megapascals 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.No manuscript containing cold-pressed walnut oil in its binding medium was 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.Adopting an explicit nominal GDP level target always strengthens market expectations of long-term real output stability.
  • 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.Every script possessing a fixed inventory of exactly 65 discrete graphemic characters represents an open-syllable writing system rather than a morphosyllabic one.

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
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Topics

Sufficient Assumption

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