GATE 2015 CS (CS3) – Question 26

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

A room contains truth-tellers and liars. An unknown person tosses a fair coin unseen and says: “The result is head if and only if I am telling the truth.” Which is correct?

The result is head
The result is tail
If the person is a liar, the result is tail
If the person is truthful, the result is tail

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Correct answer: (A) The result is head

Explanation

Let H mean heads and T that the person tells the truth. The spoken proposition is H↔T and must have truth value T. If T is true, H↔true must be true, forcing H. If T is false, H↔false must be false, again forcing H. Hence heads in either case, A.

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