The statement pattern $(p \land q) \to (r \lor \sim s)$ is false. Then the truth values of $p, q, r$ and $s$ are respectively

  • A
    $T, F, T, T$
  • B
    $T, T, F, T$
  • C
    $T, T, T, F$
  • D
    $T, T, F, F$

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If $\sim p \lor q$ is false, then which of the following is correct?

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 $12 \times 3 = 36$.
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$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.

The logical equivalent of $p \Leftrightarrow q$ is :-

Consider the following statements:
Statement $1$: If a quadrilateral is a square,then all of its sides are equal.
Statement $2$: If all the sides of a quadrilateral are equal,then it is a square.

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