If the inverse of the conditional statement $p \to \left( { \sim q\ \wedge  \sim r} \right)$ is false, then the respective truth values of the statements $p, q$ and $r$ is

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

The converse of the statement "If $p < q$, then $p -x < q -x"$ is -

Negation of "If India wins the match then India will reach in the final" is :-

Which one of the following is a tautology ?

Consider the following statements :

$A$ : Rishi is a judge.

$B$ : Rishi is honest.

$C$ : Rishi is not arrogant.

The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is