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Which one of the following statements is FALSE?

1. p ^ ~(p v q) is a tautology (always true)
2. p -> q is logically equivalent to ~p v q
3. (p v q) ^ (q v r) is true when p, q, r are T, F, T respectively
4. ~(p ^ (q v r)) is equivalent to (~p v ~q) ^ (~p v ~r)

Correct answer: p ^ ~(p v q) is a tautology (always true)

Solution

p ^ ~(p v q) = p ^ ~p ^ ~q, which contains p ^ ~p (a contradiction), so it is always false, not always true; hence that statement is wrong.

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