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

Let $p, q, r$ denote arbitrary statements. Then the logically equivalent of the statement $p\Rightarrow (q\vee r)$ is

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:

The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to

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

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