The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:

The proposition $\left( { \sim p} \right) \vee \left( {p\, \wedge  \sim q} \right)$

Negation of the statement : - $\sqrt{5}$ is an integer or $5$ is irrational is

The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee  \sim \left( {p\, \vee q} \right)$ is logically equivalent to

The logical statement $[ \sim \,( \sim \,P\, \vee \,q)\, \vee \,\left( {p\, \wedge \,r} \right)\, \wedge \,( \sim \,q\, \wedge \,r)]$ is equivalent to

The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to