GATE 2015 CS (CS2) – Question 11

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 1 mark · Multiple choice

S1: If a candidate is known to be corrupt, he will not be elected. S2: If a candidate is kind, he will be elected. Which follows logically?

If a person is known corrupt, he is kind
If a person is not known corrupt, he is not kind
If a person is kind, he is not known corrupt
If a person is not kind, he is not known corrupt

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Correct answer: (C) If a person is kind, he is not known corrupt

Explanation

Write C→¬E and K→E. Contraposition of the first gives E→¬C. Combining K→E→¬C yields “kind implies not known corrupt”, C. The other options reverse implications or assert relationships not entailed by the premises.

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