$p$ and $q$ are two logical statements. If $r: p \rightarrow (\sim p \vee q)$ has truth value false,then the truth values of $p$ and $q$ are respectively:

Let $p, q, r$ be three logical statements. Consider the compound statements $S_{1}: ((\sim p) \vee q) \vee ((\sim p) \vee r)$ and $S_{2}: p \rightarrow (q \vee r)$. Then,which of the following is $NOT$ true?

If $(p \wedge \sim r) \rightarrow (\sim p \vee q)$ has truth value $F$,then the truth values of $p, q,$ and $r$ are respectively:

The conditional statement $(p \wedge q) \implies p$ is:

If $p : 5$ is not greater than $2$ and $q : \text{Jaipur is the capital of Rajasthan}$ are two statements,then the negation of the statement $p \Rightarrow q$ is:

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