College algebra and trigonometry, global edition, Edition: by Lial, Margaret L

By Lial, Margaret L

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Extra info for College algebra and trigonometry, global edition, Edition: 6th edition

Example text

The rectangle in the drawing represents the universal set U. Such a diagram is a Venn diagram. Two sets A and B are equal whenever A ⊆ B and B ⊆ A. Equivalently, A = B if the two sets contain exactly the same elements. For example, B U Aʕ B 51, 2, 36 = 53, 1, 26 Figure 1 is true because both sets contain exactly the same elements. However, 51, 2, 36 ≠ 50, 1, 2, 36 because the set 50, 1, 2, 36 contains the element 0, which is not an element of 51, 2, 36. EXAMPLE 3 Examining Subset Relationships Let U = 51, 3, 5, 7, 9, 11, 136, A = 51, 3, 5, 7, 9, 116, B = 51, 3, 7, 96, C = 53, 9, 116, and D = 51, 96.

D) U contains the element 13, but A does not. Therefore, U = A is false. ■ ✔ Now Try Exercises 53, 55, 63, and 65. A A؅ A؅ Figure 2 Operations on Sets Given a set A and a universal set U, the set of all elements of U that do not belong to set A is the complement of set A. For example, if set A is the set of all students in a class 30 years old or older, and set U is the set of all students in the class, then the complement of A would be the set of all students in the class younger than age 30.

13y - 5213y + 5219y 2 - 252 68. 1t + 421t + 421t - 421t - 42 Find each product. See Examples 8 and 9. 69. 12m + 3212m - 32 70. 18s - 3t218s + 3t2 73. 14m + 2n22 74. 1a - 6b22 71. 14x 2 - 5y214x 2 + 5y2 75. 15r - 3t 222 77. 312p - 32 + q4 2 79. 313q + 52 - p4313q + 52 + p4 81. 313a + b2 - 14 2 83. 1y + 223 85. indd 59 72. 12m3 + n212m3 - n2 76. 12z 4 - 3y22 78. 314y - 12 + z4 2 80. 319r - s2 + 24 319r - s2 - 24 82. 312m + 72 - n4 2 84. 1z - 323 86. 1r + 324 26/08/16 10:28 am 60 CHAPTER R Review of Basic Concepts Perform the indicated operations.

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