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Dr. Jaffe Advanced Mathematics Review Sheet NAME: _____________________________________________ 1. Let U = {1, 2, 3, 4, 5} with A = {1, 2, 3}, B = {3, 4}, and C = {1, 2, 3, 4}. a) Create a Venn Diagram b) Which sets are subsets of each other? 2. Which of the following sets are equal? Explain. a) {1, 2, 3} b) {3, 2, 1, 3} c) {3, 1, 2, 3} d) {1, 2, 2, 3} 3. a) If set A has 63 proper sets, what is |A|? Explain. b) If a set B has 64 sets of odd cardinality, what is |B|? Explain. 4. Let A = {1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 17, 18}. How many subsets of A contain 6 elements? 5. Give an example of three sets W, X, Y such that W ∈ X and X ∈ Y, but W ∉ Y. 6. When U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, and C = { 7, 8, 9}, find a) A ∩ B b) A ∪ B c) B ∩ C d) A ∪ C ∩ B 7. For U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, let A = {1, 2, 3, 4, 5}, B = {1, 2, 4, 8}, C = {1, 2, 3, 5, 7}, and D = {2, 4, 6, 8}. Determine each of the following: a) (A ∪ B) ∩ D Μ b) πΆΜ ∪ π· c) A ∪ (B – C) d) B – (C – D) e) Μ Μ Μ Μ Μ Μ Μ Μ πΆ∩π· f) A ∪ (B ∩ C) 8. Use a membership table to establish each of the following: a) Μ Μ Μ Μ Μ Μ Μ π΄ ∩ π΅ = π΄Μ ∪ π΅Μ Μ Μ Μ ∩ πΆ) = (π΄ ∩ π΅Μ ) ∪ (π΄Μ ∪ πΆΜ ) b) Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ Μ (π΄ ∩ π΅) ∪ (π΄ 9. Using the laws of set theory, simplify each of the following: a) π΄ ∩ (π΅ − π΄) b) π΄Μ ∪ π΅Μ ∪ (π΄ ∩ π΅ ∩ πΆΜ )