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Q)

# Which of the following is a contradiction ?

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

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A)
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.