Statement-1: If A and B are two events such that P(A)=1, then A and B are independent.

Statement-2: A and B are two independent events iff

$P(A ∩ B) = P(A) P(B)$

Statement 1 is True, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

Clearly, statement-2 is true. (see Theory)

If $P(A)=1$, then $ P(\overline{A})=0$

Now, $\overline{A} ∩ B ⊂ \overline{A}$

$⇒ P(\overline{A} ∩ B) ≤ P(\overline{A})$

$⇒ P(\overline{A} ∩ B) ≤ 0$

$⇒ P(\overline{A} ∩ B) = 0$

$⇒ P(\overline{A} ∩ B) = P(\overline{A})P(B)$    $[∵ P(\overline{A})=0]$

$⇒(\overline{A})$ and B are independent events.

⇒ A and B are independent events.