Algebra for College Students by Mark Dugopolski

By Mark Dugopolski

Algebra for college kids, 5e is a part of the newest choices within the winning Dugopolski sequence in arithmetic. The author’s aim is to give an explanation for mathematical innovations to scholars in a language they could comprehend. during this publication, scholars and school will locate brief, particular factors of phrases and ideas written in comprehensible language. the writer makes use of concrete analogies to narrate math to daily reports. for instance, while the writer introduces the Commutative estate of Addition, he makes use of a concrete analogy that “the cost of a hamburger plus a Coke is equal to a Coke plus a hamburger”. Given the significance of examples inside of a math e-book, the writer has paid shut awareness to an important information for fixing the given subject. Dugopolski incorporates a double cross-referencing process 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 simply supply caliber, but in addition an excellent volume of routines and functions. The Dugopolski sequence is understood for delivering scholars and college with the main volume and caliber of workouts in comparison to the other developmental math sequence out there. In finishing this revision, Dugopolski feels he has built the clearest and so much concise developmental math sequence out there, and he has performed so with out comprising the fundamental info each pupil must turn into profitable in destiny arithmetic classes.

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73. 74. 75. 76. 77. 78. 79. 80. 81. 82. B ϭ ͕4, 5, 6, 7, 8, 9} D ϭ ͕2, 4, 6, 8͖ AʜB AʜC AʝB AʝC (A ʝ B) ʜ D (A ʝ C) ʜ D (A ʜ B) ʜ D (B ʜ C) ʝ A (B ʝ C) ʝ A (B ʝ D) ʝ C (B ʝ D) ʜ (C ʝ D) (A ʜ B) ʝ (C ʜ D) Write each set using set-builder notation. Answers may vary. 83. ͕3, 4, 5, 6͖ 84. ͕1, 3, 5, 7͖ 85. ͕5, 7, 9, 11, . 2 86. ͕4, 5, 6, 7, . ͖ 9 92. Cooperative learning Work with a small group to answer the following questions. If A ʕ B and B ʕ A, then what can you conclude about A and B? If (A ʜ B) ʕ (A ʝ B), then what can you conclude about A and B?

D ʜ F) ʝ E 59. D ʜ (E ʝ F) 60. D ʜ (F ʝ E ) 61. (D ʝ F) ʜ (E ʝ F) 62. (D ʝ E) ʜ (F ʝ E) 64. (D ʜ F) ʝ (D ʜ E) 17. A ʜ C 18. A ʜ B 63. (D ʜ E) ʝ (D ʜ F) 19. A ʝ C 21. B ʜ C 20. A ʝ B 22. B ʝ C Miscellaneous 23. 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.

22. ͕y Ϳ y is a whole number greater than 0͖ 5. What are the real numbers? 23. ͕x Ϳ x is an integer between Ϫ3 and 5͖ 6. What is the ratio of the circumference and diameter of any circle? 24. ͕y Ϳ y is an integer between Ϫ4 and 7͖ U1V The Rational Numbers Determine whether each statement is true or false. Explain your answer. See Example 1. 7. Ϫ2 ʦ N 9. 0 ʦ Q 8. Ϫ2 ʦ Q 10. 025, 0, ͙2 ෆ, 3 ᎏ , ᎏ A ϭ Ϫ͙10 2 2 2 11. 95 ʦ Q 12. 333 . . ʦ Q 13. Q ʕ Z 14. Q ʕ N 1 15. ᎏ2ᎏ ʦ Z are members of these sets.

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