Which of the following is an open statement

  • A

    $x$ is a natural number

  • B

    Give me a glass of water

  • C

    Wish you best of luck

  • D

    Good morning to all

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Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

Statement $-1$ : The statement $A \to (B \to A)$ is equivalent to $A \to \left( {A \vee B} \right)$.

Statement $-2$ : The statement $ \sim \left[ {\left( {A \wedge B} \right) \to \left( { \sim A \vee B} \right)} \right]$ is a Tautology

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Which Venn diagram represent the truth of the statement“All students are hard working.”

Where $U$ = Universal set of human being, $S$ = Set of all students, $H$ = Set of all hard workers.

$(\sim (\sim p)) \wedge q$ is equal to .........

The contrapositive of the statement "If it is raining, then I will not come", is

  • [JEE MAIN 2015]