1. Let AU), 3,11) denote the set {b,b+s,b+28, . . . ,b+(n1)s}. For instance, A(2, 3, 4) = {'2, 5,8, 11}. The variable names suggest b for beginning and s for skip value. (a) Write out the set A(1[},3,5). (h) Write out the set AU, 6, T). (c) Prove or disprove: Every element of AU, 6, 7) is prime. (d) What is the book's notation for the set A((], 1,6)? (e) Write out the set AU, 6, 7) A(10, 3, 5). (f) Write out the set A(2, 3, 4) U A((], 1, 6). (g) Write out the set A(2, 3, 4) x A(2, 3, 4). Bonus: Find values for b and s such that every elements of AU), 3, 5] is prime. 2. A logical staternent f (P, Q) is called a tautology if it is true for every combination of truth values for P and Q. A logical staternent f (P, Q) is called a contradiction if it is false for every combination of truth values for P and Q. (Please use the book's ordering of I} and 1 values for truth tables.) (a) Show that [P =) Q] A [P A -Q) is a contradiction. (b) Show that [PA (P =- (2)) =- Q is a tautology. (c) Show that P =) [Q =~ R) and (P A Q) => R are logically equivalent. 3. Logic with words. (a) Give the contrapositive of the statement, \"If it's Tuesday, then I have class." ('0) Explain why both the original statement and the contrapositive in (a) are true for you. (c) Give the converse of the statement, \"If it's Tuesday, then I have class." (d) Explain why the converse in (c) is false for you. (e) What can you say about a student's schedule for whom the converse in (c) is true? (f) What is the negation of \"every good boy does fun\"? (g) Prove or disprove: (3 n E Z) (Vm E Z) n