2. Let f: A → B and g: C → D be functions. The product of f and g is the function defined as follows: (f 9] (x, y) = (f (x),f (y)) for every (r, y) E Ax C. Prove that f g is a function from Ax C to B x D. Prove that if f and g are injective, then f g is injective, and if f and g are surjective, then fg is surjective.

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