102 Chapter 2 Linear Equations and Inequalities in One Variable Solutions 1a. Set Graph Interval A –1 0 1 2 3 4 5 6 7 8 9 (-∞, 7 {x | x ≤ 7} B –1 0 1 2 3 4 5 6 7 8 9 1, ∞) {x | x ≥ 1} A B –1 0 1 2 3 4 5 6 7 8 9 –1 0 1 2 3 4 5 6 7 8 9 1, 7 {x | 1 ≤ x ≤ 7} So, A B = 1, 7. 1b. Set Graph Interval A –3 –2 –1 0 1 2 3 4 5 6 7 (3, ∞) {x | x > 3} B –3 –2 –1 0 1 2 3 4 5 6 7 (0, ∞) {x | x > 0} A B –3 –2 –1 0 1 2 3 4 5 6 7 –3 –2 –1 0 1 2 3 4 5 6 7 (3, ∞) {x | x > 3} So, A B = (3, ∞). 1c. Set Graph Interval A –2 –1 0 1 2 3 4 5 6 7 8 4, ∞) {x | x ≥ 4} B –2 –1 0 1 2 3 4 5 6 7 8 (-∞, 2 {x | x ≤ 2} A B –2 –1 0 1 2 3 4 5 6 7 8 –2 –1 0 1 2 3 4 5 6 7 8 { } Notice that the two sets do not overlap; therefore, there is no intersection. So, A B is the empty set, or . Student Check 1 Find the intersection of the sets. Draw the graph of the intersection and write each solution set in interval notation and set-builder notation. a. A = 5, ∞) and B = (-∞, 6) b. A = (-∞, -1) and B = (-∞, -4) c. A = (-∞, -3) and B = (5, ∞) The Union of Sets We will now examine another operation on sets called the union. The union of sets is the joining together of the elements from each set. The word “union” conjures up images of joining together people or things for a common purpose. For instance, groups of players come together to form a team, and workers often join unions to have someone look out for their interests. Furthermore, when two people get married, they form a union of sorts. Objective 2 ▶ Determine the union of two sets.
hendricks_intermediate_algebra_1e_ch1_3
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