Let $X$ and $Y$ are two events such that $P(X \cup Y=P)\,(X \cap Y).$

Statement $1:$ $P(X \cap Y' = P)\,(X' \cap Y = 0).$

Statement $2:$ $P(X) + P(Y = 2)\,P\,(X \cap Y)$

  • [AIEEE 2012]
  • A

    Statement $1$ is false, Statement $2$ is true.

  • B

    Statement $1$ is true, Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$ .

  • C

    Statement $1$ is true, Statement $2$ is false

  • D

    Statement $1$ is true, Statement $2$ is true;Statement $2$ is a correct explanation of Statement $1.$

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  • [IIT 2002]

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