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(Answers for Chapter 0: Preliminary Topics) A.0.1 CHAPTER 0: Preliminary Topics SECTION 0.1: SETS OF NUMBERS 1) ± 12 is an integer. ± 12 , 5 7 , and 7.13 are rational numbers. All the listed numbers are real numbers. 2) ± 12 is an integer, or ± 12 is in the set of integers. True. 3) ± is not in the set of rational numbers. (Since is real, that means that is an irrational number.) True. 4) ± denotes “such that.” ± denotes “for all” or “for every.” ± denotes “there exists.” 5) Set-builder Form Graphical Form Interval Form x ± ± ² 1 < x ³ 2 {} ± 1, 2 ( ² ³ x ± ± x ²³ 3 ± 3, ² ³ ´ ) x ± ± x < 0 ±² ,0 () 6) Set-builder Form Graphical Form Interval Form x ± ± x 2 , ± 2 ³± 2, ² 7) a) 2, 4 ( ± ² , b) 3, 9 [] 8) If T ± T , then, by the definition of T , T ± T , which is a contradiction. If T ± T , then, by the definition of T , T ± T , which is a contradiction.

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(Answers for Chapter 0: Preliminary Topics) A.0.2 SECTION 0.2: LOGIC 1) a) If Arnold is an American, then Arnold is a Californian. False; Arnold could be an Alabaman (for example). b) If Arnold is not a Californian, then Arnold is not an American. False; Arnold could be an Alabaman (for example). c) If Arnold is not an American, then Arnold is not a Californian. True. d) Its contrapositive 2) Yes 3) No 4) False. The following is true: x 2 = 9 ± x = ² 3o r x = 3 () . SECTION 0.3: ROUNDING 1) a) 42.4, b) 42.40, c) 42.397, d) 42.3972 2) Decimal Number of Decimal Places Number of Significant Digits (or Figures) 7.583 3 4 0.00510 5 3 600.0020 4 7 SECTION 0.4: ABSOLUTE VALUE AND DISTANCE 1) a) ± , b) 0, c) 7.5 2) a = a ,i f a ± 0 ² a f a < 0 ³ ´ µ 3) x ± a , or a ± x
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