2.3 Venn Diagrams, Set Operations, and Data Representation 61 Our next example involves both the intersection and the complement of sets. Solution a) The elements that are common to both set A and set B, are a c , , and e. Therefore, = A B a c e {, , }. > b) The elements that are common to both set B and set C are b and d. Therefore, = B C b d {, }. > c) There are no elements that are common to both set A and set C. Therefore, = A C {}. > 7 Now try Exercise 15 Example 4 Intersection and Complement Given U A B {1, 2, 3, 4, 5, 6} {2, 3, 5, 6} {2, 4, 6} = = = Determine a) ′ A B > b) ′A B > c) ′ ′ A B > d) ′ A B ( ) > Solution a) First determine ′B, the set of elements in the universal set that are not in set B. ′ = B {1, 3, 5}, then ′ = = A B {2, 3, 5, 6} {1, 3, 5} {3, 5}. > > b) First determine ′A, the set of elements in the universal set that are not in set A. ′ = A {1, 4}, then ′ = = A B {1, 4} {2, 4, 6} {4}. > > c) From parts b) and a), respectively, we have ′ = A {1, 4} and ′ = B {1, 3, 5}. Then, ′ ′ = = A B {1, 4} {1, 3, 5} {1} > > d) First determine A B > which is the set of elements that are common to both set A and set B. = = A B {2, 3, 5, 6} {2, 4, 6} {2, 6} > > Next, ′ A B ( ) > is the set of elements that are in the universal set that are not in A B. > 7 ′ = A B ( ) {1, 3, 4, 5} > Now try Exercise 17 Note, from Example 4 parts c) and d) that, in general, ′ ′ ≠ ′ A B A B ( ) . > > We will discuss the relationship between such sets further in Section 2.4. Union The word union means to unite or join together, and that is exactly what is done when we perform the operation of union. Definition: Union The union of set A and set B, symbolized by A B, < is the set containing all the elements that are members of set A or of set B (or of both sets).
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