1. Using the following definition to draw a state diagram. (Show your work.) (30 points) A finite automaton A,-(Q, , , qo, F} where Q = {go, qi, q2, q3, q4), = {a, b, c), is described as qil goo q qe is the start state, and 2. Examine the following formal descriptions of sets so that you understand which members they contain. Write a short informal English description of each set. (3 points each) a. 13, 6, 9, 12,. b. {n l n = 10m, for some m in N} 3. Write formal descriptions of the following sets. (3 points each) a. The set containing all integers that are greater than 100 b. The set containing the string abba c. The set containing nothing at all 4. Let A be the set (w, x, y, z) and B be the set (x. y). (3 points each) a. What are the subsets of B? b. What is AUB c. What is AnB d. What is AXB e. What is the power set of B? S. f A has a elements and B has b elements, how many elements are in A X B? Explain your answer. (3 pointse Conurinht 2017 C Lin