The logical expression $[p \wedge (q \vee r)] \vee [(\sim p \wedge q) \vee (\sim p \wedge r)]$ is equivalent to

The statement $[(p \wedge q)$ $\rightarrow p]$ $\rightarrow (q \wedge \sim q)$ is

Which of the following is $NOT$ equivalent to $p \rightarrow q$?

Check the validity of the statement given below by the method specified against it.
$p:$ The sum of an irrational number and a rational number is irrational (by contradiction method).

Let $p$ and $q$ stand for the statements "$2 \times 4 = 8$" and "$4$ divides $7$" respectively. Then the truth values of the following biconditional statements are:
$(i)$ $p \leftrightarrow q$
$(ii)$ $\sim p \leftrightarrow q$
$(iii)$ $\sim q \leftrightarrow p$
$(iv)$ $\sim p \leftrightarrow \sim q$

Let,$p$: Ramesh listens to music.
$q$: Ramesh is out of his village.
$r$: It is Sunday.
$s$: It is Saturday.
Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as: