Which of the following statement$(s)$ is/are not true?
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.

  • A
    Only $I$ and $IV$
  • B
    Only $I$
  • C
    Only $II$ and $III$
  • D
    Only $I$, $II$ and $IV$

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The negation of $p \rightarrow (\sim p \vee q)$ is

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

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If the truth value of $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is false, then which of the following is $NOT$ true?

The biconditional statement $p \Leftrightarrow q$ is equivalent to:

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