Consider the following two statements. S_1: If a candidate is known to be corrupt, then he will not be elected. S_2: If a candidate is kind, he will be elected. Which one of the following statements follows from S_1 and S_2 as per sound inference rules of logic? A. If a person is known to be corrupt, he is kind B. If a person is not known to be corrupt, he is kind C. If a person is kind, he is not known to be corrupt D. If a person is not kind, he is not known to be corrupt

GATE 2015 · Discrete Mathematics · Logical Reasoning · medium

Answer: Kind -> NOT Corrupt follows from S_1 and S_2. Answer: C.

1. Take contrapositive of S_1: S_1: C -> NOT E. Contrapositive: NOT (NOT E) -> NOT C, i.e., E -> NOT C. So: if a person is elected, they are not known to be corrupt.
2. Apply Hypothetical Syllogism with S_2: S_2 gives K -> E. Contrapositive of S_1 gives E -> NOT C. Chaining: K -> E -> NOT C, so K -> NOT C. In words: if a person is kind, they are not known to be corrupt. This is option C.