Answer
Converse: $\forall$ real numbers x, if x>0, then $x^2 \geq 1.$
Inverse: $\forall$ real numbers x, if $x^2 < 1$, then x $\leq$ 0.
Contrapositive: $\forall$ real numbers x, if x $\leq$ 0, then $x^2 < 1$.
All statements are false.
Counterexamples:
Contrapositive: Let x=-2, then $x^2 = 4$ which is not less than 1. (since the contrapositive is logically equivalent to the original statement, the original statement is also false)
Inverse: Let x= 1/2. Then $x^2 = 1/4 < 1$, but x is not less than or equal to 0.
Converse: Let x= 1/2. Then x>0, but $x^2 =1/4$ is not greater than or equal to 1.
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).
