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Soru

Zorluk: OrtaMust Be True / Most Strongly Supported

Geochemists studying paleoclimate records in subterranean cave formations have established the following premises:

• Every stalagmite specimen from the Hanlin formation that preserves intact lipid biomarkers exhibits depleted δ18O\delta^{18}\text{O} isotopic ratios.
• Any stalagmite specimen from this formation that has undergone calcite recrystallization fails to preserve intact lipid biomarkers.
• A stalagmite specimen exhibits depleted δ18O\delta^{18}\text{O} isotopic ratios only if it formed during an era of elevated precipitation.
• Analysis of Hanlin specimen H-4 confirms that it preserves intact lipid biomarkers.

If the statements above are true, which one of the following must be true on the basis of them?

  1. A
    Any stalagmite specimen from the Hanlin formation that formed during an era of elevated precipitation preserves intact lipid biomarkers.
  2. B
    Any stalagmite specimen from the Hanlin formation that has not undergone calcite recrystallization exhibits depleted δ18O\delta^{18}\text{O} isotopic ratios.
  3. Hanlin specimen H-4 formed during an era of elevated precipitation.Cevap
  4. D
    No stalagmite specimen from the Hanlin formation that lacks intact lipid biomarkers formed during an era of elevated precipitation.
  5. E
    Calcite recrystallization is the only process that prevents the preservation of intact lipid biomarkers in the Hanlin formation.

Cevap

Hanlin specimen H-4 formed during an era of elevated precipitation.
The stimulus provides a direct deductive chain. We are told that Hanlin specimen H-4 possesses intact lipid biomarkers. According to the first premise, any specimen with intact lipid biomarkers exhibits depleted δ18O\delta^{18}\text{O} isotopic ratios. According to the third premise, exhibiting depleted δ18O\delta^{18}\text{O} isotopic ratios occurs 'only if' the specimen formed during an era of elevated precipitation, meaning that elevated precipitation is a necessary condition for depleted ratios. Chaining these validly (L→D→PL \rightarrow D \rightarrow P) proves conclusively that specimen H-4 must have formed during an era of elevated precipitation.

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1
Translate the conditional rules and specific factual premise from the stimulus into formal logical statements.
Let LL = preserves intact lipid biomarkers, DD = exhibits depleted δ18O\delta^{18}\text{O} isotopic ratios, RR = undergone calcite recrystallization, and PP = formed during an era of elevated precipitation. The premises establish: (1) L→DL \rightarrow D, (2) R→¬LR \rightarrow \neg L (or L→¬RL \rightarrow \neg R), (3) D→PD \rightarrow P ('DD only if PP'), and (4) Fact: L(H-4)L(\text{H-4}) is true.
Formalizing the statements eliminates ambiguity regarding sufficient and necessary indicators such as 'every', 'any', and 'only if'.
2
Chain the conditional relationships starting from the known factual premise regarding specimen H-4.
From L(H-4)L(\text{H-4}) and rule (1) L→DL \rightarrow D, we deduce D(H-4)D(\text{H-4}). From D(H-4)D(\text{H-4}) and rule (3) D→PD \rightarrow P, we deduce P(H-4)P(\text{H-4}).
Applying modus ponens across the valid transitive chain L→D→PL \rightarrow D \rightarrow P yields the deductively guaranteed conclusion that H-4 formed during an era of elevated precipitation.
3
Evaluate the remaining options to confirm they either represent invalid formal fallacies or introduce unwarranted assumptions.
All alternative options commit classic logical errors such as conditional reversal, mistaken negation, or conflating sufficient conditions with exclusive causes.
Ensures that exactly one option is logically guaranteed by the premises.

Anahtar Kavram

Conditional Logic Chaining and Valid Deductive Inferences
Tahmini Süre:1m 15s
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Must Be True / Most Strongly Supported

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