The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to

Negation of the conditional : “If it rains, I shall go to school” is

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

If the Boolean expression $( p \Rightarrow q ) \Leftrightarrow( q *(\sim p ))$ is a tautology, then the Boolean expression $p *(\sim q )$ is equivalent to

If $q$ is false and $p\, \wedge \,q\, \leftrightarrow \,r$ is true, then which one of the following statements is a tautology?

Let $p$ and $q$ be any two logical statements and $r:p \to \left( { \sim p \vee q} \right)$. If $r$ has a truth value $F$, then the truth values of $p$ and $q$ are respectively