If A and B are independent events, then which of the following statements are TRUE?

(A) $P(A ∩ B) = P(A).P(B)$
(B) $P(A ∩ B) = P(A) - P(B)$
(C) $P(A ∪ B) = P(A) + P(B) - P(A).P(B)$
(D) $P(A ∩ B) = P(A).P(B|A)$

Choose the correct answer from the options given below:

(A), (C) and (D) only

The correct answer is Option (3) → (A), (C) and (D) only

(A) $P(A ∩ B) = P(A).P(B)$ (True)
(B) $P(A ∩ B) = P(A) - P(B)$ (False)
(C) $P(A ∪ B) = P(A) + P(B) - P(A).P(B)$ (True)
(D) $P(A ∩ B) = P(A).P(B|A)$ (True)

Given that $A$ and $B$ are independent events, evaluate the truth of each statement:

(A) $P(A \cap B) = P(A) \cdot P(B)$

True. By definition of independence.

(B) $P(A \cap B) = P(A) - P(B)$

False. This is not generally true.

(C) $P(A \cup B) = P(A) + P(B) - P(A) \cdot P(B)$

True. Since $P(A \cap B) = P(A) P(B)$ for independent events, this follows from the general formula:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

(D) $P(A \cap B) = P(A) \cdot P(B|A)$

True. This is the definition of conditional probability, always true.