This exercise concerns subgroups of Z x Z. a. Let C1 = {(a, b) ∈ Zx Z | a = b} Show that C1 is asubgroup of Z x Z.
b. For each positive integer n >= 2, let Cn = {(Cn ={(a, b) ∈ Z x Z|a b (mod n)}.Show that Cn is a subgroup of Z x Z.
c. Show that every subgroup of Z xZ that contains C1 has the formCn, for some positive integer n.