Which of the following quantified statements is true?

  • A
    The square of every real number is positive
  • B
    There exists a real number whose square is negative
  • C
    There exists a real number whose square is not positive
  • D
    Every real number is rational

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The expression $\sim ( \sim p \to q)$ is logically equivalent to

The output of the following circuit is

The proposition $(\sim p) \vee (p \wedge \sim q)$ is equivalent to

The logical expression $p \wedge (\sim p \vee \sim q) =$ ?

Statement-$I$: $\sim (p \leftrightarrow q)$ is equivalent to $(p \wedge \sim q) \vee (q \wedge \sim p)$.
Statement-$II$: $p$ $\rightarrow (p$ $\rightarrow q)$ is a tautology.

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