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JEE Math Practice Question

Consider the following two propositions: $$P1: \sim (p \to \sim q)$$ $$P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)$$ If the proposition $$p \to (( \sim p) \vee q)$$ is evaluated as FALSE, then :

  1. A.P1 is TRUE and P2 is FALSE
  2. B.P1 is FALSE and P2 is TRUE
  3. C.Both P1 and P2 are FALSE
  4. D.Both P1 and P2 are TRUE

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