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Set Operations and Venn Diagrams 2.2 – 2.3 Intersection of Sets The intersection of sets A and B, denoted by A B , is the set of all elements that are common to both. That is, A B {x | x A and x B} . Union of Sets The union of sets A and B, denoted by A B , is the set of all elements that are either in A or B or in both. That is, A B {x | x A or x B} . Let A = {1,2,3,4,5}, B = {1,3,4,6}, and C = {1,6,7}. Find the following: 1 c. B C = {1, 6} 2 a. A B = {1, 2, 3, 4, 5, 6} 3 b. A ( B C ) = {1, 2, 3, 4, 5, 6} A 2 5 B 3 4 1 6 7 C U Complement of a Set Let Ų be the universal set, and let A be a subset of U . The complement of A, denoted by A’, is the set of elements in U that are not in A. That is, A' {x | x U and x A}. This set is also symbolized by U – A . Let U = {a,b,c,d,e,f}, A = {a,c,e}, B = {b,d,e,f}, and C = {a,b,d,f}. Find each specified set. 16 b. ( A B)' = {a, b, c, d, f} 17 a. ( A B)' = Ø 18 a. ( A B) C' = {c, e} 19 b. C ( A B)' = {a, b, c, d, f} Difference of Sets If A and B are two sets, the difference of A and B, denoted by A – B, is the set of all elements that are in A and not in B. That is, A - B {x | x A and x B}. Let U = {1,2,3,4,5}, A = {2,3,4}, and B = {1,4,5}. Find each specified set. 27 b. U B = {2, 3} 28 b. B A = {1, 5} A B 5 2 4 3 1 U Use the numbered regions of the diagram below to identify each specified set. a. A B = {1,2, 3,5,6,7} b. B C = {6,7} c. A B C = {7} d. B ' = {1,4,5,8} e. A C B = {1,4,5}