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),ƒ (y)) for every (x, y) E Ax C. Prove that f.g is a function from A x C to B...

Extracted text: 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),ƒ (y)) for every (x, y) E Ax C. Prove that f.g is a function from A x 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 f·g is surjective.