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Question

If P and Q are two statements, then which of the following compound statements is a tautology?

A
((PQ)Q)P
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B
((PQ)Q)P
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C
((PQ)Q)(PQ)
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D
((PQ)Q)Q
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Solution

The correct option is B ((PQ)Q)P
(PQ)Q
(PQ)Q
PQ)(QQ)
(PQ)(QQ)
(PQ)

Now,
(1) (PQ)P
(PQ)P
PQ

(2) (PQ)P
(PQ)P
T

(3) (PQ)(PQ)
(PQ)(PQ)
PQ

(4) (PQ)Q
(PQ)Q
PQ

Thus, ((PQ)Q)P is a tautology.

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