Write the negation of the following statement and check whether the resulting statement is true:
There does not exist a quadrilateral which has all its sides equal.

$\sim ((\sim p) \wedge q)$ is equivalent to

Which one of the following Boolean expressions is a tautology?

If $(\sim p \wedge q) \rightarrow r$ is false,then the truth values of $p, q, r$ are respectively:

Let $F_{1}(A, B, C) = (A \wedge \sim B) \vee [\sim C \wedge (A \vee B)] \vee \sim A$ and $F_{2}(A, B) = (A \vee B) \vee (B \rightarrow \sim A)$ be two logical expressions. Then ...... .

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.