4. Let U := Letters in the English Alphabet = {a, b, c, ...,x, y, z} A = {t, r, i, a, n, g, I, e, s} B = {s, q, u, a, r, e }, C = {h, e, x, a, g, o, n, s } %3D Determine the following: (a) AU(BnC) (b) (AUBYNC (c) (AnC)u(BnC) (d) An (Cnuy (e) n[(AU B)n (BUuC)]

Real Analysis 1

Set Theory, Proving

cartesian product Write out the indicated sets in list notation. (A ×B) ×B

(a) Let f : Z × Z → Z be the function f(m, n) = m²n + n. Is ƒ one-t0-one? Is f onto? Justify your answer. (b) Let f : N –→ N be the function f(n) = 2n + 2. Is f one-to-one? Is f onto? Justify your answer. (c) Let f(x) = x³ + 2x + 1, g(x) = sin x, h(x) = x² + 2. Write down explicitly the formulas for (h ogo f)(x) and (fogoh)(x).