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Question

Statement - 1: (pq) is equivalent to pq.
Statement - 2: (pq) is a tautology.

A
Statement - 1 is true, Statement - 2 is true;
Statement - 2 is not a correct explanation for statement - 1.
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B
Statement - 1 is true, Statement - 2 is false.
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C
Statement - 1 is false, Statement - 2 is true.
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D
Statement - 1 is true, Statement - 2 is true,
Statement - 2 is a correct explanation for statement - 1.
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Solution

The correct option is B Statement - 1 is true, Statement - 2 is false.
The truth table for the logical statements, involved in statement 1, is as follows:
pqqpq(pq)pqTTFFTTTFTTFFFTFTFFFFTFTT
We observe the columns for (pq) and pq are identical, therefore
(pq) is equivalent to pq
But (pq) is not a tautology as all entries in its column are not T.
Statement - 1 is true but statement - 2 is false.

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