\[\begin{array}{1 1}(1)p\vee q&(2)p\wedge q\\(3)p\vee\sim p&(4)p\wedge\sim p\end{array}\]

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a)If p is F and q is F then $p \vee q$ is F

$\therefore p \vee q $ is not a tautology

b)If p is F and q is F then $p \wedge q$ is F

$\therefore p \wedge q $ is not a tautology

c)If p is T then $ \sim p $ is F

then $p \vee \sim p$ is T.

If P is F then $\sim p$ is T

then $ p \vee \sim p$ is T

$\therefore p \vee p $ is a tautology

d)If p is T then $ \sim p $ is F

then $p \wedge \sim p$ is F

If p is F then $\sim p$ is T

then $p \wedge$ is F.

$\therefore p \wedge \sim p$ is not a tautology

Hence 3 is the correct answer.

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