The contrapositive of the statement “If you are born in India, then you are a citizen of India”, is

  • [JEE MAIN 2019]
  • A

    If you are a citizen of India, then you are born in India

  • B

    If your are not a citizen of India, then you are not born in India

  • C

    If you are no born in India, then you are not a citizen of India

  • D

    If you are born in India, then you are not a citizen of India

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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

  • [JEE MAIN 2013]

$(p\rightarrow q) \leftrightarrow (q \vee  ~ p)$ is

Negation of $p \wedge( q \wedge \sim( p \wedge q ))$ is

  • [JEE MAIN 2023]

Which of the following statement is a tautology?

The converse of the statement "If $p < q$, then $p -x < q -x"$ is -