If $A$ and $B$ are independent events, then which of the following is/are true?

(A) $\bar A$ and $B$ are independent events
(B) $P(A ∩ B) = 0$
(C) $\bar A$ and $\bar B$ are independent events
(D) $P(A ∩ B) = P(A) + P(B)$

Choose the correct answer from the options given below:

(A) and (C) only

The correct answer is Option (1) → (A) and (C) only

Given: A and B are independent events.

(A) Ā and B: Yes, independent events remain independent even if one is complemented.

(B) P(A ∩ B) = 0: No, this would mean A and B are mutually exclusive, which contradicts independence unless one is zero.

(C) Ā and B̄: Yes, complements of independent events are also independent.

(D) P(A ∩ B) = P(A) + P(B): No, this is only true for mutually exclusive events, not independent ones.

Correct options: (A), (C)