Question: Consider sets A = {a, b, c}, B = {m, n} and D = {x, y} (a) Find all possible functions f : A B.

Consider sets A = {a, b, c}, B = {m, n} and D = {x, y}

(a) Find all possible functions f : A B.

(b) Find all injective functions f : A D, if any, or explain why there is none.

(d) Give an example of a bijective function g : B D, showing the inverse.

(e) Find all surjective functions f : D B, if any, or explain why there is none.

(f) If function g : A B is a constant function, with g(c) = n, and h : B D is not a constant function, compute all possible composite functions h g : A D.

(g) Suppose that E is the set of all subsets of set A. In other words, E is the powerset of A. How many elements does E contain? Find all injective functions f : E A, if any, or explain why there is none.

Thank you.

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