If the truth value of the statement $(P \wedge(\sim R)) \rightarrow((\sim R) \wedge Q)$ is $F$, then the truth value of which of the following is $F$ ?
$P \vee Q \rightarrow \sim R$
$R \vee Q \rightarrow \sim P$
$\sim( P \vee Q ) \rightarrow \sim R$
$\sim( R \vee Q ) \rightarrow \sim P$
The logically equivalent preposition of $p \Leftrightarrow q$ is
Statement$-I :$ $\sim (p\leftrightarrow q)$ is equivalent to $(p\wedge \sim q)\vee \sim (p\vee \sim q) .$
Statement$-II :$ $p\rightarrow (p\rightarrow q)$ is a tautology.
Contrapositive of the statement “If two numbers are not equal, then their squares are not equals” is
Negation of the statement $P$ : For every real number, either $x > 5$ or $x < 5$ is
Which of the following statements is $NOT$ logically equivalent to $\left( {p \to \sim p} \right) \to \left( {p \to q} \right)$?