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

Which of the following statement patterns is a tautology?

The proposition $p \Rightarrow \sim (p \wedge \sim q)$ is

If the truth value of the compound statement $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is false, then the truth values of $p \to q$ and $q \to p$ are respectively...

The statement pattern $(p \wedge q) \wedge [\sim r \vee (p \wedge q)] \vee (\sim p \wedge q)$ is equivalent to $......$

If the truth value of the Boolean expression $((p \vee q) \wedge (q$ $\rightarrow r) \wedge (\sim r))$ $\rightarrow (p \wedge q)$ is false,then the truth values of the statements $p, q, r$ respectively can be: