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

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a)If p is T and q is T

then $p \vee q $ is T

$\therefore p \vee q$ cannot be a contradiction

b)If p is T and q is T

then $p \wedge q $ is T

$\therefore p \wedge q$ cannot be a contradiction

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

$\therefore p \vee \sim p$ not a contradiction

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

then $p \wedge \sim p$ is F

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

$\therefore p \wedge \sim p$ is contradiction

Hence 4 is a correct answer.

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