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The Statement that is $TRUE$ among the following is
The contrapositive of $3x + 2 = 8 \Rightarrow x = 2$ is $x\ne 2$ $\Rightarrow 3x + 2\ne 8.$
The converse of $tan\,x\,=0\,\Rightarrow x = 0$ is $x\ne 0\,\Rightarrow tan\,x = 0.$
$p \Rightarrow q$ is equivalent to $p\, \vee \, \sim \,q.$
$p \vee q$ and $p\, \wedge \,q$ have the same truth table.
Solution
Only statement given in option
$(a)$ is true.
$(b)$ The converse of
$\tan \,x = 0 \Rightarrow x = 0$ is
$x = 0 \Rightarrow \tan \,x = 0$
$\therefore $ Statement $(b)$ is false
$(c)$ $ \sim \left( {p \Rightarrow q} \right)$ is equivalent to ${p \wedge \sim q}$
$\therefore $ Statement given in option $(c)$ is false.
$(d)$ No, ${p \vee q}$ and ${p \wedge q}$ does not have the same truth vale.
