Find the component statements of the following and check whether they are true or not.
Chandigarh is the capital of Haryana and $UP$.

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.

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

Identify the quantifier in the following statement and write the negation of the statement.
For every real number $x, x$ is less than $x+1.$

The negation of the statement "If a quadrilateral is a square,then it is a rhombus" is:

If the truth value of the statement pattern $(\sim p \land q) \lor (\sim p \land \sim q) \lor (p \land \sim q)$ is $F$, then the truth values of $(p \lor \sim q)$ and $(p \to q)$ are ... respectively.