1. (10) Determine whether the following expressions are sets or families of sets. In these expressions, A and B are sets, F and B are families of sets, and {Ai : i I} and {Bi : i I} are indexed families of sets. You do not need to show your work. T a. A ( F ). family sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m set b. {Ap : p I is prime}. set family S T c. ( F ) ( G). set family d. P(A) {Bi : i I}. family Th set e. P ( S (F G)). set family 1 https://www.coursehero.com/file/7427500/3202f11-mid2/ Th sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 2. (30) Prove that for all integers n, n2 + n is even. 2 https://www.coursehero.com/file/7427500/3202f11-mid2/ Th sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 3. (30) Prove that for all sets A and B, if A B A then B A. 3 https://www.coursehero.com/file/7427500/3202f11-mid2/ S F 6 S G then there is some A F Th sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 4. (30) Let F and G be families of sets. Prove that if such that for all B G, A 6 B. 4 https://www.coursehero.com/file/7427500/3202f11-mid2/ sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Th 5 https://www.coursehero.com/file/7427500/3202f11-mid2/ NAME : sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m MHF 3202 Sets and Logic Fall 2011 October 14, 2011 Midterm 2 Instructions: This is a closed book exam and no notes are allowed. You are not to provide or receive help from any outside source during the exam except that you may ask the instructor for clarification of a problem. You have 50 minutes and you should attempt all problems. Print your name in the space provided. Sign the FERPA release on the next page only if you wish your exam returned in lecture. Calculators or other computing devices are not allowed. Th Except where indicated, you must show all work and give a reason (or reasons) for your answer. A correct answer with incorrect work will be considered wrong. https://www.coursehero.com/file/7427500/3202f11-mid2/ FERPA Release: Because of privacy concerns, I will not return your graded exams in lecture without your permission. If you want me to return your exam in lecture, please sign on the line indicated below. Otherwise, you may collect your exam during my office hours. SIGN HERE: . Points 1 10 2 30 3 30 4 30 Total 100 Projected Grade Score sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Problem Th Note: The projected grade listed above is an estimate of the grade you would receive if the course ended right now. https://www.coursehero.com/file/7427500/3202f11-mid2/ Powered by TCPDF (www.tcpdf.org)