Assignment1solution(0211)

Assignment1solution(0211) - MATH 0211 Basic Applicable...

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MATH 0211: Basic Applicable Mathematics Suggested Solution for Assignment 1 1. (a) The solution set for equation ( x - 5)( x 2 + 1 . 5 x - 1) = ( x - 5)( x - 0 . 5)( x + 2) = 0 is {- 2 , 0 . 5 , 5 } . Note that x N is required, thus we have { x N : ( x - 5)( x 2 + 1 . 5 x - 1) = 0 } = { 5 } with cardinality 1. (b) with cardinality 0. (c) { 83 , 89 } with cardinality 2. (d) {- 1 , 0 , 10 } with cardinality 3. (e) { 2 , 3 } with cardinality 2. 2. Represent the following sets by set builder notations or listing: (a) { 0 } (b) { x R : 2 < x 4 } (or (2 , 4] using interval notation) (c) { 0 , 4 , 5 , 6 } (d) { x R : 2 < x 4 or 8 < x < 10 } (or (2 , 4] (8 , 10) using interval notation) 3. (a) ∅ ⊆ A (b) A B (c) B 6 = D (or B 6⊆ D , D 6⊆ B ) (d) A C = B (e) B C = C . 4. (1) ( A B ) c = {- 1 , - 2 , - 3 , 1 , 2 , 3 } c = { 0 } , A c B c = { 0 , 1 , 2 , 3 }∩{ 0 , - 1 , - 2 , - 3 } = { 0 } Thus we have ( A B ) c = A c B c . (2) ( A B ) c = c = U , A c B c = { 0 , 1 , 2 , 3 } ∪ { 0 , - 1 , - 2 , - 3 } = U Thus we have ( A B ) c = A c B c 5. (a) A B = { x U : x is a multiple of 50 } (b) n ( A B ) = n ( A ) + n ( B ) - n ( A B ) = 100 + 40 - 20 = 120 6. (a) S is the circle with radius 1 centered at the origin. B is the circular disk (including the boundary) with radius 1 centered at the origin. (b) I S = (1 / 2 , 1 / 2) , ( - 1 / 2 , - 1 / 2) , I B = ( x, y ) R : y = x, - 1 / 2 x 1 / 2 . 7. Suppose set M represents the students taking Mathematics, set B represents the stu- dents taking Biology, and set
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