GATE | GATE-CS-2015 (Set 2) | Question 13

Consider the following two statements.

S1: If a candidate is known to be corrupt, then he will not be elected.
S2: If a candidate is kind, he will be elected.

Which one of the following statements follows from S1 and S2 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 not 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


Answer: (C)

Explanation:

S1: If a candidate is known to be corrupt, then 
    he will not be elected.
S2: If a candidate is kind, he will be elected.

If p → q, then ¬q → ¬p
So from S1, elected → not corrupt
and S2 is,   kind → elected

Therefore, kind → not corrupt


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