The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee  \sim \left( {p\, \vee q} \right)$ is logically equivalent to

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $p \nabla q \Rightarrow(( p \nabla$q) $\nabla r$ ) is a tautology. Then (p $\nabla q ) \Delta r$ is logically equivalent to

The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to

The negative of $q\; \vee \sim (p \wedge r)$ is

The statement "If $3^2 = 10$ then $I$ get second prize" is logically equivalent to