Let F : N → N be the mapping defined by F(n) = n + 1 for all n ∈ N = {0, 1, 2, 3, . . .}, and let I : N → N be the identity mapping defined by I(n) = n for all n ∈ N.

(a) Show that there does not exist any mapping G : N → N which satisfies F ◦ G = I.

(b) Construct one example (or several examples) of mapping H : N → N which satisfies H ◦ F = I.