Q1. Let U = {1,2,3,4,5,6,7,8} be the universal set. Let A = {1,2,5,6}. Let B = {3,4,6,8}. Let C = {1,6,7,8}. Determine the following sets. In your solution for each part include at least one intermediate step. (a) BNC (b) AN(BUCQC) (c) AUC (d) (AnC)-B Q2. Prove the following statements. (a) Yae N,Fbe N, (2ab) | (e +2b+1) (b) Let S = {900z : z Z and 250 + b is odd. (b) For all integers a and b, if 4 | (a? + 7b%), then 5a + b is even