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(D) We are given that $P(A \cup B) = P(A \cap B)$.Since $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, we substitute the given condition:$P(A \cap B) = P(

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$P(A) + P(B) = 1$

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(D) We are given that $P(A \cup B) = P(A \cap B)$.Since $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, we substitute the given condition:$P(A \cap B) = P(A) + P(B) - P(A \cap B)$$2P(A \cap B) = P(A) + P(B)$.Also, since $A \cap B \subseteq A \subseteq A \cup B$ and $A \cap B \subseteq B \subseteq A \cup B$, the condition $P(A \cup B) = P(A \cap B)$ implies $P(A) = P(B) = P(A \cap B)$.This means $P(A \cap B') = P(A) - P(A \cap B) = 0$ and $P(A' \cap B) = P(B) - P(A \cap B) = 0$.Thus, options $A$, $B$, and $C$ are true.However, $P(A) + P(B) = 2P(A \cap B)$, which is not necessarily equal to $1$. Therefore, option $D$ is not true.

If $A$ and $B$ are two events of a random experiment such that $P(A \cup B) = P(A \cap B)$, then which one amongst the following four options is not true?

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