The statement $[(p \wedge  q) \rightarrow p] \rightarrow (q \wedge  \sim q)$ is

Let $p$ and $q$ be two statements.Then $\sim( p \wedge( p \Rightarrow \sim q ))$ is equivalent to

Which one of the following Boolean expressions is a tautology?

For integers $m$ and $n$, both greater than $1$ , consider the following three statements
$P$ : $m$ divides $n$
$Q$ : $m$ divides $n^2$
$R$ : $m$ is prime,
then true statement  is

Negation of $p \wedge (\sim q \vee \sim r)$ is -

If $(p \wedge \sim q) \wedge r  \to \sim r$ is $F$ then truth value of $'r'$ is :-