1-5 - Instructors Manual to Accompany FUNAMENTAL METHODS OF...

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Instructor’s Manual to Accompany FUNAMENTAL METHODS OF MATHEMATICAL ECONOMICS Fourth Edition Alpha C. Chiang and Kevin Wainwright September 2005
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Contents CONTENTS 1 CHAPTER 2 6 Ex e r c i s e2 .3. ........................................... 6 e r c i s .4. 6 e r c i s .5. 7 CHAPTER 3 9 e r c i s e3 .2. 9 e r c i s 9 e r c i s 10 e r c i s 11 CHAPTER 4 13 e r c i s e4 .1. 13 e r c i s 14 e r c i s 15 e r c i s 17 e r c i s 19 e r c i s .6. 20 e r c i s .7. CHAPTER 5 22 e r c i s e5 22 e r c i s 23 e r c i s 24 e r c i s 25 e r c i s 26 e r c i s 27 e r c i s 29 CHAPTER 6 32 1
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Ex e r c i s e6 .2. ........................................... 32 e r c i s .4. e r c i s .5. e r c i s .6. 33 e r c i s .7. 34 CHAPTER 7 35 e r c i s e7 .1. 35 e r c i s e r c i s .3. 37 e r c i s e r c i s 38 e r c i s 39 CHAPTER 8 40 e r c i s e8 41 e r c i s 43 e r c i s 44 e r c i s 45 e r c i s 47 CHAPTER 9 51 e r c i s e9 51 e r c i s e r c i s 52 e r c i s 54 e r c i s 55 CHAPTER 10 56 e r c i s e10 .1 . .......................................... 56 e r c i s .2 . e r c i s .3 . 57 e r c i s .4 . 58 2
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Ex e r c i s e10 .5 . .......................................... 59 e r c i s .6 . 60 e r c i s .7 . 61 CHAPTER 11 63 e r c i s e11 .2 . 63 e r c i s .3 . 64 e r c i s .4 . 66 e r c i s 69 e r c i s 71 e r c i s 73 CHAPTER 12 76 e r c i s e12 76 e r c i s 77 e r c i s 78 e r c i s 82 e r c i s 83 e r c i s 85 CHAPTER 13 87 e r c i s e13 .1 . 87 e r c i s 88 e r c i s 90 e r c i s 91 CHAPTER 14 93 e r c i s e14 93 e r c i s 94 e r c i s 95 e r c i s 96 e r c i s 97 CHAPTER 15 99 3
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Ex e r c i s e15 .1 . .......................................... 99 e r c i s .2 . e r c i s .3 . 101 e r c i s .4 . 102 e r c i s .5 . 103 e r c i s .6 . 104 e r c i s .7 . 105 CHAPTER 16 108 e r c i s e16 108 e r c i s 109 e r c i s 111 e r c i s 112 e r c i s 113 e r c i s 115 e r c i s 116 CHAPTER 17 118 e r c i s e17 118 e r c i s 119 e r c i s e r c i s 121 e r c i s 122 CHAPTER 18 124 e r c i s e18 124 e r c i s 126 e r c i s e r c i s 128 CHAPTER 19 131 e r c i s e19 131 e r c i s 133 e r c i s 135 4
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Ex e r c i s e19 .5 . .......................................... 137 e r c i s .6 . 139 CHAPTER 20 142 e r c i s e20 .2 . 142 e r c i s .4 . 144 5
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CHAPTER 2 Exercise 2.3 1. (a) { x | x> 34 } (b) { x | 8 <x< 65 } 2. True statements: (a), (d), (f), (g), and (h) 3. (a) {2,4,6,7} (b) {2,4,6} (c) {2,6} (d) {2} (e) {2} (f) {2,4,6} 4. All are valid. 5. First part: A ( B C )= { 4 , 5 , 6 } { 3 , 6 } = { 3 , 4 , 5 , 6 } ;and ( A B ) ( A C { 3 , 4 , 5 , 6 , 7 } { 2 , 3 , 4 , 5 , 6 } = { 3 , 4 , 5 , 6 } too. Second part: A ( B C { 4 , 5 , 6 } { 2 , 3 , 4 , 6 , 7 } = { 4 , 6 } ( A B ) ( A C { 4 , 6 } { 6 } = { 4 , 6 } too. 6. N/A 7. , { 5 } , { 6 } , { 7 } , { 5 , 6 } , { 5 , 7 } , { 6 , 7 } , { 5 , 6 , 7 } 8. There are 2 4 =16 subsets: , {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}, and {a,b,c,d}. 9. The complement of U is ˜ U = { x | x/ U } . Here the notation of ”not in U ”isexpressedv iathe / symbol which relates an element ( x )toa set ( U ). In contrast, when we say ” is a subset of U,” the notion of ”in U” is expressed via the symbol which relates a subset( )toaset ( U ). Hence, we have two di f erent contexts, and there exists no paradox at all. Exercise 2.4 1. (a) {(3,a), (3,b), (6,a), (6,b) (9,a), (9,b)} (b) {(a,m), (a,n), (b,m), (b,n)} (c) { (m,3), (m,6), (m,9), (n,3), (n,6), (n,9)} 2. {(3,a,m), (3,a,n), (3,b,m), (3,b,n), (6,a,m), (6,a,n), (6,b,m), (6,b,n), (9,a,m), (9,a,n), (9,b,m), (9,b,n),} 6
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3. No. When S 1 = S 2 . 4. Only (d) represents a function.
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1-5 - Instructors Manual to Accompany FUNAMENTAL METHODS OF...

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