1. Let A be the set {e, f, g, h} and B be the set {e, g, h}. a. Is A a subset of B? b. Is Ba subset of A? c. What is A U B? d. What is A x B? e. What is the power set of B? 2. Determine whether these statements are true or false? a. E (} b. () (} c. {} c {0, {}} d. E {0, {}} e. E {, (), {}} 3. Find the power set these sets, wh a and b tinct elements. eac a. {a} b. {a, b} c. {{0. (}} d. {} e. (. { } 4. What is the cardinality of each of these sets? a. {a} b. {a. (a}} c. {{a}) d. (a, {a}, {a, {a}} e. {a, {}, {a}} 5. State whether the following quantified statements are true over the set of natural numbers N = {1, 2, 3, 4, }: a. Vx ay [x= y? +1] b. 3x vy [x+ y> 0] 6. Let Li = {a, b} and Lz = {ab, aab, aaab}. Define the following: !3! a. Li U L: b. Li o Lz c. Lz* d. Li* e. (Li U L:)* 7. Exhibit a string over the alphabet (a, b} that does not belong to the language a"b* U a"(abba)