19 R.2 Sets and Real Numbers EXAMPLE 6 Finding Unions ofTwo Sets Find each of the following. (a) 51, 2, 5, 9, 146´51, 3, 4, 86 (b) 51, 3, 5, 76´52, 4, 66 (c) 51, 3, 5, 7, c6´52, 4, 6, c6 SOLUTION (a) Begin by listing the elements of the first set, 51, 2, 5, 9, 146. Then include any elements from the second set that are not already listed. 51, 2, 5, 9, 146´51, 3, 4, 86 = 51, 2, 3, 4, 5, 8, 9, 146 (b) 51, 3, 5, 76´52, 4, 66 = 51, 2, 3, 4, 5, 6, 76 (c) 51, 3, 5, 7, c6´52, 4, 6, c6 = N Natural numbers S Now Try Exercises 71 and 83. The set operations are summarized below. Set Operations Let A and B define sets, with universal set U. The complement of set A is the set A′ of all elements in the universal set that do not belong to set A. A′ = 5x∣ x{U, xoA6 The intersection of sets A and B, written A¨B, is made up of all the elements belonging to both set A and set B. A∩B = 5x∣ x{A and x{B6 The union of sets A and B, written A∪B, is made up of all the elements belonging to set A or to set B (or to both). A∪B = 5x∣ x{A or x{B or x{both A and B6 Sets of Numbers and the Number Line As mentioned previously, the set of natural numbers is written in set notation as follows. 51, 2, 3, 4, N6 Natural numbers Including 0 with the set of natural numbers gives the set of whole numbers. 50, 1, 2, 3, 4, N6 Whole numbers Including the negatives of the natural numbers with the set of whole numbers gives the set of integers. 5 N, −3, −2, −1, 0, 1, 2, 3, N6 Integers Integers can be graphed on a number line. See Figure 12. Every number corresponds to one and only one point on the number line, and each point corresponds to one and only one number. The number associated with a given point is the coordinate of the point. This correspondence forms a coordinate system. –5 0 1 2 3 4 5 –4 –3 –2 Graph of the Set of Integers –1 Origin Figure 12
RkJQdWJsaXNoZXIy NjM5ODQ=