Which of the following is wrong statement?

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p→q is logically equivalent ~p∨q

If the truth values of p, q, r are T, F, T respectively, then the truth value of (p∨q)∧(q∨r) is T

~(∨q∨q∨r)≅∼p∧~q∧~r

The truth value of p∧~(p∨q) is always T

answer is D.

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Detailed Solution

The truth tables of p→q and ~p∨q are given belowClearly, truth tables of p→q and ~p∨q are same. So, p→q is logically equivalent to ~p∨q. Hence, option (a) is correct. If the truth value of p, q, r are T, F, T respectively, then the truth values of p v g and q v r are each equal to T. Therefore, the truth value of (p∨q)∧(q∨r) is T. Hence, option (b) is correct.We know that, ~(p∨q∨r)≅(~p∧~q∧~r) So, option (c) is correct.If p is true and q is false, then p∨q is true.Consequently~(p∨q) is false and hence p∧~(p∨q) isfalse.Hence, option (d) is wrong.

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