Difficulty: Easy
Correct Answer: Some textbooks written by Prabhakar are published by ABC Publishing Company.
Explanation:
Introduction / Context:This is a basic syllogism problem about set relations. We are told that every book by Prabhakar falls inside the set “textbooks,” and that a subset of Prabhakar’s books are published by ABC Publishing Company. We must determine what conclusion necessarily follows.
Given Data / Assumptions:
Concept / Approach:Translate to sets: Let P = {Prabhakar’s books}. Let T = {textbooks}. Let A = {books published by ABC}. P is a subset of T (P ⊆ T). P ∩ A is non-empty (because “some of his books are published by ABC”). Therefore, the intersection P ∩ A consists of textbooks (since P ⊆ T).
Step-by-Step Solution:
From P1: every element of P is in T.From P2: there exists at least one element in P that is also in A.Therefore: there exists at least one book that is both in T and A and is by Prabhakar.Hence, “Some textbooks written by Prabhakar are published by ABC.”Verification / Alternative check:
Try to deny the conclusion: If none of the ABC-published Prabhakar books were textbooks, P1 would be violated. So the conclusion must be true.Why Other Options Are Wrong:
A: Claims ABC publishes only textbooks—too strong.B: Adds “other than ABC,” which is not derivable.D: Says all ABC books are by Prabhakar—unsupported.E: Introduces “critical essays,” not mentioned in the premises.Common Pitfalls:
Confusing “all P are T” with “all T are P.” Only the first is given.Final Answer:Some textbooks written by Prabhakar are published by ABC Publishing Company.
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