The statement "If $3^2 = 10$ then $I$ get second prize" is logically equivalent to

For the statement: "If a quadrilateral $ABCD$ is a rhombus,then its opposite sides are parallel",its contrapositive and converse are respectively given by:

Are the following pairs of statements negations of each other:
$1$. The number $x$ is not a rational number.
$2$. The number $x$ is not an irrational number.

Find the component statements of the following compound statement and check whether they are true or false.
Number $3$ is prime or it is odd.

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 $T$ and that of $r$ and $s$ are $F$,then the truth values of $a$ and $b$ are respectively...

Check whether the following statement is true or not.
If $x, y \in \mathbb{Z}$ are such that $x$ and $y$ are odd,then $xy$ is odd.