The negation of $(p \land q) \to ((p \lor r) \to \sim q)$ is equivalent to ...

If the statement pattern $(p \wedge q) \rightarrow (r \vee \sim s)$ is false,then the truth values of $p, q, r$ and $s$ are respectively:

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:

Which of the following statements is true?

Write the contrapositive of the following statement:
If you are born in India,then you are a citizen of India.

The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$