Section 1.5 Compound Inequalities 85 55. The revenue R for selling x fleece jackets is given by the equation The cost to produce x jackets is Find the number of jackets that the company needs to sell to produce a profit. (Hint:A profit occurs when revenue exceeds cost.) 56. The revenue R for selling x mountain bikes is The cost to produce x bikes is C 56,000 140x. Find the number of bikes that the company needs to sell to produce a profit. R 249.95x. C 2300 18.50x. R 49.95x. Expanding Your Skills For Exercises 57–60, assume a b. Determine which inequality sign ( or ) should be inserted to make a true statement.Assume a 0 and b 0. 57. for 58. for a c c 6 0 a c c 7 0 ______ b c, ______ b c, 59. for 60. ac for c 7 0 ______ ac c 6 0 bc, ______ bc, Compound Inequalities Section 1.5 1. Union and Intersection of Sets Two or more sets can be combined by the operations of union and intersection. Definition of A Union B and A Intersection B The union of sets A and B, denoted A B, is the set of elements that belong to set A or to set B or to both sets A and B. The intersection of two sets A and B, denoted A B, is the set of elements common to both A and B. The concepts of the union and intersection of two sets are illustrated in Figures 1-6 and 1-7. A B A A B A union B The elements in A or B or both A B B A intersection B The elements in A and B Figure 1-6 Figure 1-7 Concepts 1. Union and Intersection of Sets 2. Solving Compound Inequalities: And 3. Solving Inequalities of the Form a x b 4. Solving Compound Inequalities: Or 5. Applications of Compound Inequalities Finding the Union and Intersection of Sets Given the sets: A {a, b, c, d, e, f} B {a, c, e, g, i, k} C {g, h, i, j, k} Find: a. A ´ B b. A ¨ B c. A ¨ C Solution: a. A ´ B {a, b, c, d, e, f, g, i, k} The union of A and B includes all the elements of A along with all the elements of B. Notice that the elements a, c, and e are not listed twice. Example 1
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