For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p\, \wedge \,q)$ is
$p \leftrightarrow q$
$\sim p\, \vee \,\sim q$
$\sim p\, \wedge \,\sim q$
$p\, \wedge \,q$
Negation of statement "If I will go to college, then I will be an engineer" is -
Which of the following pairs are not logically equivalent ?
If the truth value of the Boolean expression $((\mathrm{p} \vee \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r}) \wedge(\sim \mathrm{r})) \rightarrow(\mathrm{p} \wedge \mathrm{q}) \quad$ is false then the truth values of the statements $\mathrm{p}, \mathrm{q}, \mathrm{r}$ respectively can be:
The negation of the statement $q \wedge \left( { \sim p \vee \sim r} \right)$
The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to: