Answer
Statement: $\forall n \in \mathbb{Z}$, if n is prime, then n is odd or n=2.
Contrapositive: $\forall n \in \mathbb{Z}$, if n is not odd and $n \neq 2$, then n is not prime.
Converse: $\forall n \in \mathbb{Z}$, if n is odd or n=2, then n is prime.
Inverse: $\forall n \in \mathbb{Z}$, if n is not prime, then n is not odd and $n \neq 2$.
A prime number is a positive whole number that is divisible only by 1 and itself.
The statement and its contrapositive are logically equivalent. The statement is true, so the contrapositive is as well.
The converse and inverse are contrapositives of each other and are hence logically equivalent. The converse is false. Take as a counterexample n=-5 (n is odd and in the domain), but n is not prime because prime is defined only for positive whole numbers. Hence the converse and inverse are both false.
Work Step by Step
A statement of the form: $\forall x \in D$, if P(x) then Q(x),
has as its contrapositive statement: $\forall x \in D$, if ~Q(x) then ~P(x),
as its converse statement: $\forall x \in D$, if Q(x) then P(x),
and as its inverse statement: $\forall x \in D$, if ~P(x) then ~Q(x).
