State whether each of the following functions is injective, surjective, bijective, or none of these categories: (N is the set of natural numbers, and Σ∗ is the set of all strings over Σ.) (a) f : N → N , f(n) = n div 3 (b) g : N → N , g(n) = n2 + 2n + 1 (c) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = a|w|. (d) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = wR.

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