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]
  • A

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

  • B

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

  • C

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

  • D

    Statement $-1$ is true; Statement $-2$ is true;
    Statement $-2$ is the correct explanation for Statement $-1$

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Which of the following is the negation of the statement "for all $M\,>\,0$, there exists $x \in S$ such that $\mathrm{x} \geq \mathrm{M}^{\prime \prime} ?$

  • [JEE MAIN 2021]

The Boolean expression $(\mathrm{p} \wedge \mathrm{q}) \Rightarrow((\mathrm{r} \wedge \mathrm{q}) \wedge \mathrm{p})$ is equivalent to :

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