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

If the inverse of the conditional statement $p \to \left( { \sim q\ \wedge  \sim r} \right)$ is false, then the respective truth values of the statements $p, q$ and $r$ is

The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :

The Statement that is $TRUE$ among the following is

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

The logically equivalent preposition of $p \Leftrightarrow q$ is