Lesson 07 Quiz (Show/Explain all Work) IST 230 Set Theory 1. (This Problem Counts Double) 2. Give a formal proof that A = B: Let A be the set of all dogs bred to hunt badgers Let B be the set of all dogs who are Dachshunds Now use the following \"facts\" to give a formal proof that A = B (Hint: remember you must prove two separate things). The \"facts\" are: (1) If a dog is bred to hunt badgers, then the dog is good at digging (2) If a dog is good at digging, then the dog is a Dachshund (3) If a dog is a Dachshund, then the dog is good at digging (4) If a dog is good at digging, the dog is bred to hunt badgers 3. Explain when two sets are disjoint and give a concrete example 4. Define and explain the difference between a subset and a proper subset and give examples of each 5. (This Problem Counts Double) 6. Give a formal proof that A = B: Let A be the set of all integers x such that x is = 2k for some integer k Let B be the set of all integers x such that x = 2k+2 for some integer k Give a formal proof that A = B Tell whether or not the following are equal. HINT: look carefully at the notations used 7. (1, 2, 3, 1) = (3, 2, 1) Larry Newcomerqattachments_7be2e8971770f0eab27a82ec91501411d2febb90 (19 @ 5 each) Page 1 of 3 The Online Course Content and textbook are the ONLY sources of help that may be used for this exam Lesson 07 Quiz (Show/Explain all Work) IST 230 Set Theory 8. {1, 2, 3, 1} = {3, 2, 1} 9. (1, 2, 3, 1) = (1, 2, 3, 4) Let A = {a, b, c} B = {1, 3} 10. Calculate A x B x C = 11. Calculate C = {5, 6} C x A Let b} A = {3, 4, 5, a} B = {g, h, i} 12. Calculate A C = 13. Calculate A B = 14. Calculate C = {4, 5, a, b} and the Universal Set U = {3, 4, 5, g, h, i, a, A - C = 15. Give an example of a partition of set U 16. Calculate AC (the set complement of A) = 17. Give an example of sets that are NOT a partition of the set {1, 2, 3, 4, 5}, then explain why they do not form a partition 18. (This Problem Counts Double) 19. As discussed in the Online Course Content, there are 5 possible relationships between any two given sets A and B. Describe these 5 possible cases as per the Lesson: a. Larry Newcomerqattachments_7be2e8971770f0eab27a82ec91501411d2febb90 (19 @ 5 each) Page 2 of 3 The Online Course Content and textbook are the ONLY sources of help that may be used for this exam Lesson 07 Quiz (Show/Explain all Work) IST 230 Set Theory b. c. d. e. Larry Newcomerqattachments_7be2e8971770f0eab27a82ec91501411d2febb90 (19 @ 5 each) Page 3 of 3 The Online Course Content and textbook are the ONLY sources of help that may be used for this exam