If the truth value of the statement $p \to \left( { \sim q \vee r} \right)$ is false $(F)$, then the truth values of the statement $p, q, r$ are respectively
$T, T, F$
$F, T, T$
$T, F, T$
$T, F, F$
The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to
Which one of the following, statements is not a tautology
$(p\rightarrow q) \leftrightarrow (q \vee ~ p)$ is
The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to
The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :