Identify the underlying deductive reasoning pattern for each of the following valid arguments by pairing the concrete scenario with its formal structural description.
- The recently observed comet will either disintegrate upon approaching the sun or survive its perihelion passage intact. Spectroscopic analysis confirms it will not disintegrate upon approaching the sun. Therefore, the comet will survive its perihelion passage intact.Two exhaustive possibilities are posited; the ruling out of one of these possibilities leaves the remaining option as the only logically mandated conclusion.
- If the introduced crop variety is truly resilient to the regional soil fungus, it will synthesize a specific defensive glycoprotein in its root structure. However, extensive chemical assays show the variety synthesizes no such glycoprotein. Thus, the introduced variety is not truly resilient to the regional soil fungus.A conditional relationship is established, and the subsequent denial of its necessary condition guarantees the denial of its sufficient condition.
- If the average water temperature in the estuary rises by one degree, the native oyster population will decline. If the native oyster population declines, the local wading bird population will migrate further north. Therefore, if the average water temperature in the estuary rises by one degree, the local wading bird population will migrate further north.Two conditional statements are integrated by linking the necessary condition of the first to the sufficient condition of the second, yielding a continuous logical chain.
- If a patient experiences bilateral damage to the hippocampus, they will exhibit severe anterograde amnesia. The subject in the clinical study has experienced bilateral damage to the hippocampus. Therefore, the subject will exhibit severe anterograde amnesia.A rule establishes that a specific sufficient condition guarantees a resulting outcome; the fulfillment of that sufficient condition is affirmed, ensuring the outcome occurs.
Answer
The arguments correctly pair based on their logical frameworks: The comet argument uses elimination (Disjunctive Syllogism). The crop argument denies the necessary condition (Modus Tollens). The estuary argument links two conditional statements (Hypothetical Syllogism). The patient argument affirms the sufficient condition (Modus Ponens).
Each provided argument represents a distinct, fundamentally valid form of deductive logic. Correctly matching them requires translating the concrete scenario into its abstract logical skeleton: Disjunctive Syllogism (A or B; not A; therefore B), Modus Tollens (If A then B; not B; therefore not A), Hypothetical Syllogism (If A then B; if B then C; therefore if A then C), and Modus Ponens (If A then B; A; therefore B).
Step-by-Step Solution
Key Concept
Parallel Valid Structure