Find the component statements of the following and check whether they are true or not.
All prime numbers are either even or odd.

By giving a counterexample,show that the following statement is not true.
$p:$ If all the angles of a triangle are equal,then the triangle is an obtuse-angled triangle.

Consider the statement patterns:
$A$. $(q \to p) \lor (p \to q)$
$B$. $(\sim p \lor \sim q) \leftrightarrow \sim (p \land q)$
$C$. $[(p \lor q) \land \sim p] \land \sim q$
$D$. $(p \land q) \land (\sim p \lor \sim q)$
Which of the following is true?

If $p \rightarrow (p \wedge \neg q)$ is false,then the truth values of $p$ and $q$ are respectively

If $p$ and $q$ are true and $r$ and $s$ are false statements,then which of the following is true?

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is: