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) (
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This note was uploaded on 01/02/2012 for the course MATH 0211 taught by Professor Chan during the Spring '10 term at HKU.

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

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