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Question

For the statements p and q, consider the following compound statements :
(a) (q (pq))p
(b) ((pq)p)q
Then which of the following ststements is correct ?

A
(a) is a tautology but not (b).
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B
(a) and (b) both are not tautologies.
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C
(a) and (b) both are tautologies.
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D
(b) is a tautology but not (a).
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Solution

The correct option is C (a) and (b) both are tautologies.
(a) pqqpqq(pq)p(q(pq))pTTFTFFTTFTFFFTFTFTFTTFFTTTTT

(a) is tautology.

(b) pqpqp(pq)p((pq)p)qTTTFFTTFTFFTFTTTTTFFFTFT

(b) is tautology.
(a) and (b) both are tautologies.

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