1. The Language of a 2-State DFA Let M = (1, 2, 8,90,F) be a DFA and put L = L(M). By considering the different possibilities for the set of final states F of M, prove that if Q consists of exactly two states, then one of the following hold (note that (b) and (c) are not mutually exclusive): (a) L is empty. (b) L contains the empty string. (c) L contains a string of length 1