Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

  • [AIEEE 2009]
  • [JEE MAIN 2013]
  • A

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

  • B

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

  • C

    Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$

  • D

    Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$

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$\left( { \sim \left( {p \vee q} \right)} \right) \vee \left( { \sim p \wedge q} \right)$ is logically equivalent to 

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Statement$-II :$  $p\rightarrow (p\rightarrow q)$ is a tautology.

The contrapositive of $(p \vee q) \Rightarrow r$ is

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