Simplify $(p \vee q) \wedge (p \vee \sim q)$

The negation of the statement "The number is an odd number if and only if it is divisible by $3$."

The equivalent statement of "If three vertices of a triangle are represented by cube roots of unity,then the triangle is an equilateral triangle" is

If $p \to (q \lor \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \land r$ and $\sim p \to \sim q$ are :

The converse of the statement "If $p < q$,then $p - x < q - x$" 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...