The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to

If the Boolean expression $( p \wedge q ) \circledast( p \otimes q )$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by

The negation of the compound proposition $p \vee (\sim p \vee q)$ is

The contrapositive of the statement “If you are born in India, then you are a citizen of India”, is

If $p$ : It rains today, $q$ : I go to school, $r$ : I shall meet any friends and $s$ : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.

$\sim (p \Rightarrow q) \Leftrightarrow \sim p\; \vee \sim q$ is