The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to
$(\sim x \wedge y) \vee(\sim x \wedge \sim y)$
$(x \wedge \sim y) \vee(\sim x \wedge y)$
$(x \wedge y) \vee(\sim x \wedge \sim y)$
$(x \wedge y) \wedge(\sim x \vee \sim y)$
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 statement $( p \rightarrow( q \rightarrow p )) \rightarrow( p \rightarrow( p \vee q ))$ is
Let $*, \square \in\{\wedge, \vee\}$ be such that the Boolean expression $(\mathrm{p} * \sim \mathrm{q}) \Rightarrow(\mathrm{p} \square \mathrm{q})$ is a tautology. Then :
The following statement $\left( {p \to q} \right) \to $ $[(\sim p\rightarrow q) \rightarrow q ]$ is
The statement $p \rightarrow (q \rightarrow p)$ is equivalent to