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

The negation of the statement $(p \vee q)^{\wedge}(q \vee(\sim r))$ is

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

If $p$ and $q$ are simple propositions, then $p \Leftrightarrow \sim \,q$ is true when

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

Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is