The statment $ \sim \left( {p \leftrightarrow  \sim q} \right)$ is

Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ 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$?$

Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard

The statement $( p \wedge q ) \Rightarrow( p \wedge r )$ is equivalent to.

Negation of the statement $P$ : For every real number, either $x > 5$ or $x < 5$ is