If $q$ is false and $p\, \wedge \,q\, \leftrightarrow \,r$ is true, then which one of the following statements is a tautology?

  • [JEE MAIN 2019]
  • A

    $(p\, \vee \,r\,)\, \to \,(p\, \wedge \,r)$

  • B

    $(p\, \wedge \,r\,)\, \to \,(p\, \vee \,r)$

  • C

    $p\, \wedge \,r$

  • D

    $p\, \vee \,r$

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  • [JEE MAIN 2023]

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