Let $a : \sim (p \wedge \sim r) \vee (\sim q \vee s)$ and $b : (p \vee s) \leftrightarrow (q \wedge r)$. If the truth values of $p$ and $q$ are true and that of $r$ and $s$ are false,then the truth values of $a$ and $b$ are respectively:

Given below are two statements:
$p: 25 \text{ is a multiple of } 5.$
$q: 25 \text{ is a multiple of } 8.$
Write the compound statements connecting these two statements with "And" and "Or". In both cases,check the validity of the compound statement.

Which of the following is a mathematical statement?

Find the component statements of the following compound statement:
The sky is blue and the grass is green.

The correct logical equivalences from the following are: $(I)$ $p \to (q \to r) \equiv (p \land q) \to r$ $(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$ $(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$ $(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$

Which of the following is the inverse of the proposition: "If a number is a prime then it is odd."