The Boolean expression $( p \Rightarrow q ) \wedge( q \Rightarrow \sim p )$ is equivalent to :

Consider the following two propositions:

$P_1: \sim( p \rightarrow \sim q )$

$P_2:( p \wedge \sim q ) \wedge((\sim p ) \vee q )$

If the proposition $p \rightarrow((\sim p ) \vee q )$ is evaluated as $FALSE$, then

The conditional $(p \wedge q)  \Rightarrow  p$ is :-

Which of the following is a contradiction

$(\sim (\sim p)) \wedge q$ is equal to .........

Which one of the following, statements is not a tautology