For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p\, \wedge \,q)$ is 

$p \Rightarrow q$ can also be written as

The Statement that is $TRUE$ among the following 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 contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is

Let $p , q , r$ be three logical statements. Consider the compound statements $S _{1}:((\sim p ) \vee q ) \vee((\sim p ) \vee r ) \text { and }$ and $S _{2}: p \rightarrow( q \vee r )$ Then, which of the following is NOT true$?$