Difficulty: Medium
Correct Answer: D F A
Explanation:
Introduction / Context:
This is a logical reasoning question about identifying a valid argument. You are given several general statements (A–F) about categories like “straightforward things”, “perennial things”, “cats” and “people”. You must pick a triple of statements where the first two are premises and the third is their logical conclusion, and importantly, the conclusion cannot be obtained from either premise alone.
Given Data / Assumptions:
Concept / Approach:
A valid argument must have a conclusion that follows logically from both premises together, but not from either one alone. We examine each option to see whether the third statement is forced by the first two. The correct option will show a clear two-premise syllogism where the conclusion arises from connecting them.
Step-by-Step Solution:
Step 1: Analyse option C (D F A), since it looks promising:
D: All perennial things are people.
F: Some straightforward things are perennial.
A (as a potential conclusion): Some straightforward things are people.
Step 2: From D (All perennial things are people), every perennial thing is a person.
Step 3: From F (Some straightforward things are perennial), there exists at least one thing that is both straightforward and perennial.
Step 4: Combining D and F:
If some straightforward things are perennial, and all perennial things are people, then those straightforward–perennial things are also people. Therefore, some straightforward things are people.
Step 5: This is exactly statement A. So in D F A, A is a valid conclusion from D and F.
Step 6: Check that A cannot be derived from either D or F alone:
From D alone (All perennial things are people), we do not know whether any straightforward things are perennial; so we cannot conclude A.
From F alone (Some straightforward things are perennial), we know nothing about whether perennial things are people; again we cannot conclude A.
Thus, A genuinely depends on both D and F together.
Verification / Alternative check for other options:
Option A (B C A): B and C are essentially restatements about perennial things being cats, but A talks about straightforward things being people and cannot be inferred from those premises.
Option B (C F D): From C (only cats are perennial) and F (some straightforward things are perennial), we can infer that some straightforward things are cats, not that all perennial things are people (D).
Option D (E A B): E (some straightforward things are cats) and A (some straightforward things are people) do not imply that all perennial things are cats (B), since “perennial things” are not even mentioned in those two premises.
Why Other Options Are Wrong:
In each of the incorrect options, the supposed conclusion either does not logically follow from the premises or mentions sets (like perennial things) that are not constrained enough by the premises. Only D F A forms a clean chain: perennial things → people, some straightforward things → perennial, hence some straightforward things → people.
Common Pitfalls:
Students often pick combinations where the conclusion “sounds related” but does not strictly follow from the premises. Another common error is not checking whether the conclusion can already be obtained from one premise alone, which would violate the condition given in the question. Always write the relationships in symbolic form and verify whether the conclusion genuinely uses both premises.
Final Answer:
Thus, the only valid argument in the required format is the sequence D F A.
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