Show all work please

CS 275, SPRING 18, HW 1 The Homework is due next Tuesday (Jan. 30th) at the beginning of the lecture. The work has to be done independently! Problem 1 (2 pts): For each of the statements below, determine whether it is true or false (explain your answers). (a) 0 E (r), (c) E , Problem 2 (3 pts): Let A and B be sets. Prove that (AUB) - (AnB) (A - B)U (B - A). Problem 3 (3 pts): Let An jEN j n) for n - 1,2,... What are An and 1 n=1 Recall that for any sets Bn (for n = 1,2 ), the following holds co beUB, if and only if b e By for some natural number k n=1 an bEB if and only if b e B, for all natural numbers k. Problem 4 (2 pts.): Which of the functions listed below is a bijection from R to R (provide explanations): f(x)4r g(x) =x5 + 42, h(x) = e", k(x) In(e). Extra Problem (3 pts): Prove or disprove the following two statements. (a) If f and f o g are one-to-one then g is one-to-one. (b) If g and f og are one-to-one then f is one-to-one