The symbolic form of the following circuit is (where $p$ and $q$ represent switches $S_{1}$ and $S_{2}$ being closed respectively):

  • A
    $(p \vee q) \vee (\sim p \wedge \sim q) \equiv l$
  • B
    $(p \wedge q) \vee (\sim p \wedge \sim q) \equiv l$
  • C
    $(p \vee q) \wedge (\sim p \vee \sim q) \equiv l$
  • D
    $(p \wedge q) \wedge (\sim p \vee \sim q) \equiv l$

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Consider the following statements:
$(A)$ If $3+3=7$,then $4+3=8$.
$(B)$ If $5+3=8$,then the earth is flat.
$(C)$ If both $(A)$ and $(B)$ are true,then $5+6=17$.
Which of the following statements is correct?

Which of the following logical equivalences is true?

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For the statement: "If a quadrilateral $ABCD$ is a rhombus,then its opposite sides are parallel",its contrapositive and converse are respectively given by:

Which of the following statements 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.

If $p: 25$ is an odd prime number.
$q: 14$ is a composite number and
$r: 64$ is a perfect square number.
Then which of the following statement patterns is true?

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