Answer
a. Converse: If n + 1 is an even integer, then n is a prime number that is greater than 2.
Counterexample: Let n = 15. Then n + 1 is even but n is not a prime number that is greater than 2.
b. Converse: If 2m is even, then m is an odd integer.
Counterexample: Let 2m=12. Then m=6 which is not an odd integer.
c. Converse: If two circles do not have a common center, then they intersect in exactly two points.
Counterexample: Consider the case of circles a and b. Both a and b have radius 1. The center of circle a is the origin (0,0), while the center of circle b is (2,2). Circles a and b do not have a common center and they intersect at exactly zero points.
Work Step by Step
A statement of the form: $\forall x \in D$, if P(x) then Q(x),
has as its converse statement: $\forall x \in D$, if Q(x), then P(x).
