Question 2: Let n 2 be an integer. Determine the number of strings consisting of n characters, where each character is an element of the set {a, b, 0}. Let S be a set consisting of n elements. Determine the number of ordered pairs (A, B), where A S, B S, and A B = . Let S be a set consisting of n elements. Consider ordered pairs (A, B), where A S, B S, and |A B| = 1. Prove that the number of such pairs is equal to n 3 n1 .