By Mark Dugopolski

Algebra for students, 5e is a part of the newest choices within the winning Dugopolski sequence in arithmetic. The author’s objective is to give an explanation for mathematical recommendations to scholars in a language they could comprehend. during this publication, scholars and college will locate brief, particular causes of phrases and ideas written in comprehensible language. the writer makes use of concrete analogies to narrate math to daily stories. for instance, whilst the writer introduces the Commutative estate of Addition, he makes use of a concrete analogy that “the rate of a hamburger plus a Coke is equal to a Coke plus a hamburger”. Given the significance of examples inside a math e-book, the writer has paid shut consciousness to crucial information for fixing the given subject. Dugopolski contains a double cross-referencing procedure among the examples and workout units, so irrespective of which one the scholars begin with, they'll see the relationship to the opposite. eventually, the writer reveals it very important not to merely offer caliber, but additionally a superb volume of routines and purposes. The Dugopolski sequence is understood for offering scholars and college with the main volume and caliber of workouts compared to the other developmental math sequence out there. In finishing this revision, Dugopolski feels he has built the clearest and such a lot concise developmental math sequence out there, and he has performed so with no comprising the basic info each pupil must develop into profitable in destiny arithmetic classes.

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Now do Exercises 39–50 U5V Combining Three or More Sets We know how to find the union and intersection of two sets. For three or more sets we use parentheses to indicate which pair of sets to combine first. In Example 6, notice that different results are obtained from different placements of the parentheses. E X A M P L E 6 Operations with three sets Let A ϭ ͕1, 2, 3, 4͖, B ϭ ͕2, 5, 6, 8͖, and C ϭ ͕4, 5, 7͖. List the elements of each of these sets. qxd 10/31/07 6:37 PM Page 6 6 1-6 Chapter 1 The Real Numbers Solution a) The parentheses indicate that the union of A and B is to be found first and then the result, A ʜ B, is to be intersected with C.

A ʜ л 25. A ʝ л 27. A ʝ N 24. B ʜ л 26. B ʝ л 28. A ʜ N Use one of the symbols ʦ, , ϭ, , ʜ, or ʝ in each blank to make a true statement. See Example 4. A ϭ ͕1, 3, 5, 7, 9} B ϭ {2, 4, 6, 8} C ϭ ͕1, 2, 3, 4, 5͖ N ϭ ͕1, 2, 3, . ͖ 29. 30. 31. 32. 33. 34. 35. 37. AʝB л AʝC л A B ϭ ͕1, 2, 3, 4, 5, 6, 7, 8, 9͖ A Bϭл B C ϭ ͕2, 4͖ B C ϭ ͕1, 2, 3, 4, 5, 6, 8͖ 3 AʝB 36. 3 AʝC 4 BʝC 38. 8 BʜC U4V Subsets Determine whether each statement is true or false. Explain your answer. See Example 5. A ϭ ͕1, 3, 5, 7, 9} B ϭ {2, 4, 6, 8} C ϭ ͕1, 2, 3, 4, 5͖ N ϭ ͕1, 2, 3, .

D ʜ E 52. D ʝ E List the elements in each set. 65. ͕x Ϳ x is an even natural number less than 20͖ 66. ͕x Ϳ x is a natural number greater than 6͖ 67. ͕x Ϳ x is an odd natural number greater than 11͖ 68. ͕x Ϳ x is an odd natural number less than 14͖ 69. ͕x Ϳ x is an even natural number between 4 and 79͖ 70. ͕x Ϳ x is an odd natural number between 12 and 57͖ Using the sets A, B, C, and D, list the elements in each set. If the set is empty write л. A ϭ ͕1, 2, 3, 4, 5} C ϭ {1, 3, 5, 7} 71. 72. 73. 74.

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