Let $$\Omega$$ be the sample space and $$A \subseteq \Omega$$ be an event. Given below are two statements:
(S1): If $$P(A) = 0$$, then $$A = \phi$$
(S2): If $$P(A) = 1$$, then $$A = \Omega$$
Then

Let $$\Omega$$ be the sample space and $$A\subseteq\Omega$$ an event. Since we consider the statements (S1): If $$P(A)=0$$ then $$A=\phi$$, and (S2): If $$P(A)=1$$ then $$A=\Omega$$, we proceed under the JEE finite equally likely outcomes assumption.

In this setting the probability of event $$A$$ is given by $$P(A)=\frac{|A|}{|\Omega|}$$. Consequently, if $$P(A)=0$$ then $$\frac{|A|}{|\Omega|}=0$$ implies $$|A|=0$$, which leads to $$A=\phi$$. Therefore (S1) is true.

Next, if $$P(A)=1$$ then $$\frac{|A|}{|\Omega|}=1$$, and so $$|A|=|\Omega|$$. Since $$A\subseteq\Omega$$ and both sets are finite with the same cardinality it follows that $$A=\Omega$$. This shows that (S2) is true.

In a measure-theoretic setting with continuous sample spaces these statements may fail (for example, a singleton in [0,1] has probability zero but is not empty). However, under the finite equally likely assumption used in JEE both statements hold. Therefore the correct answer is Option (3): Both (S1) and (S2) are true.