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

The negation of the compound proposition $p \vee (\sim p \vee q)$ is

If $p, q, r, s$ are statements,where:
$p: A^2-B^2=(A-B)(A+B)$ where $A, B$ are matrices and $AB \neq BA$
$q: 5 \leqslant 5$
$r: { }^8 C_1+{ }^8 C_2+{ }^8 C_3+\ldots+{ }^8 C_8=256$
$s: \text{Maximum value of } { }^8 C_r \text{ is } 70$
Which of the following statements has a truth value of true?

Statement-$I$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a contradiction.
Statement-$II$: $(p$ $\rightarrow q) \Leftrightarrow (\sim q$ $\rightarrow \sim p)$ is a tautology.

If the truth value of the statement $(P \wedge (\sim R)) \rightarrow ((\sim R) \wedge Q)$ is $F$,then the truth value of which of the following is $F$?

Which of the following statements is a tautology?