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

If $p$ and $q$ are simple propositions, then $p \Rightarrow q$ is false when

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

Statement $-1$ : The statement $A \to (B \to A)$ is equivalent to $A \to \left( {A \vee B} \right)$.

Statement $-2$ : The statement $ \sim \left[ {\left( {A \wedge B} \right) \to \left( { \sim A \vee B} \right)} \right]$ is a Tautology

Which one of the following, statements is not a tautology