Which of the following is equivalent to the Boolean expression $\mathrm{p} \wedge \sim \mathrm{q}$ ?
$\sim(\mathrm{q} \rightarrow \mathrm{p})$
$\sim \mathrm{p} \rightarrow \sim \mathrm{q}$
$\sim(\mathrm{p} \rightarrow \sim \mathrm{q})$
$\sim(p \rightarrow q)$
The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to
If $P \Rightarrow \left( {q \vee r} \right)$ is false, then the truth values of $p, q, r$ are respectively
$(p \wedge \, \sim q)\, \wedge \,( \sim p \vee q)$ is :-
Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”
Suppose $p, q, r$ are positive rational numbers such that $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is also rational. Then