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Q)

# Which of the following is a tautology?

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

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A)
a)If p is 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.