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

We are given the statements:

$$p$$: Ramesh listens to music

$$q$$: Ramesh is out of his village

$$r$$: It is Sunday

$$s$$: It is Saturday

The statement to express is: "Ramesh listens to music only if he is in his village and it is Sunday or Saturday."

The phrase "P only if Q" translates to $$P \Rightarrow Q$$. So "Ramesh listens to music only if (condition)" becomes $$p \Rightarrow \text{(condition)}$$.

Now the condition is "he is in his village and it is Sunday or Saturday." Being "in his village" is the negation of $$q$$ (since $$q$$ means "out of his village"), so this is $$\sim q$$. "It is Sunday or Saturday" is $$r \vee s$$.

So the condition is $$(\sim q) \wedge (r \vee s)$$.

Therefore the full statement is $$p \Rightarrow ((\sim q) \wedge (r \vee s))$$.

Hence, the correct answer is Option 4.