MS-Sol-EE-C12

# MS-Sol-EE-C12 - CHAPTER 12 PROBABILITY FUNDAMENTAL CONCEPTS EXERCISE 12.1 1 Section 12.1(page 159 Set notation D = cfw_a d e i m n r t n(D = 8(a E

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CHAPTER 12 PROBABILITY: FUNDAMENTAL CONCEPTS EXERCISE 12.1 Section 12.1 Set notation (page 159) 1. (a) A = {1, 6, 8} n ( A ) = 3 (b) B = {male, female} n ( B ) = 2 (c) C = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} n ( C ) = 7 (d) D = { a , d , e , i , m , n , r , t } n ( D ) = 8 2. (a) E = {–1, 1} n ( E ) = 2 (b) F = {1, 3, 8, 9, 10} n ( F ) = 5 (c) G = {… , –4, –2, 0, 2, 4, …} n ( G ) = (d) H = {2, 3, 5, 7, 11, …} n ( H ) = 3. (a) I = { x : x is a colour of the light spectrum} (b) J = { x : x is a sense organ on the head} (c) K = { x : x is one of the four main bearing directions} (d) L = { x : x is one of the four major religions} 4. (a) M = { x : x is an insect} (b) N = { x : x is a fruit} (c) P = { x : x is a positive multiple of 3} (d) Q = { x : x is the square of an integer} 5. (a) M = N (= {1, 3}) (b) P Q ( Q Q = {4, - 4}) (c) R = S (d) T and U are disjoint. (or T U = φ ) 76

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C HAPTER 12 P ROBABILITY : F UNDAMENTAL C ONCEPTS 6. (a) (i) The subsets of V are: φ , {Yes}, {No}, {Yes, No}. (ii) The subsets of W are: , {1}, {3}, {8}, {1, 3}, {1, 8}, {3, 8}, {1, 3, 8}. (b) The total number of subsets of X = 2 4 = 16 7. (a) , {courtesy}, {moral}, {incorruptness}, {shame} (b) {courtesy, moral}, {courtesy, incorruptness}, {courtesy, shame}, {moral, incorruptness}, {moral, shame}, {incorruptness, shame} (c) Imagine that “shame” is removed from Y . Then there are 3 elements left. Considering these 3 elements only, the number of subsets without “shame” = number of subsets with no element + number of subsets with 1 element + number of subsets with 2 elements + number of subsets with 3 elements = 1 + 3 + 3 + 1 = 8 Alternatively, with 3 elements in a set, the number of possible subsets = 2 3 = 8. 8. (a) U = { x : x is a country} (b) U = { x : x is an integer} 9. (a) U = { x : x is an organ of the human body} (b) U = {( x , y ) : ( x , y ) is a point on the Cartesian plane} 10. (a) (i) A B = {horse, cow, sheep, pig, dog, chicken, duck} (ii) A B = {cow, pig} (iii) A \ B = {horse, sheep, dog} (iv) B \ A = {chicken, duck} (b) 11. (a) (i) Since K H , H K = H , i.e. H K = {metal, wood, water, soil} (ii) Since K H , H K = K , i.e. H K = {water} (iii) H \ K = {metal, wood, soil} (iv) K \ H = (v) H = {fire} (vi) K = {metal, wood, fire, soil} 77
S ECTION 12.1 S ET N OTATION (b) 12. (a) X = { r , f , , t } (b) ( X Y ) = { m } = { d , r , f , s , , t } (c) X Y = { r , f , , t } { d , r , s , t } = { d , r , f , s , , t } (d) ( Y \ X ) = { f , } = { d , r , m , s , t } (e) ( X Y ) = { d , m , f, s , } = { r , t } (f) X Y = { r , f , , t } { d , r , s , t } = { r , t } 13. (a) P Q = { x : - 2 < x 3} and its graphical representation is (b) P = { x : - 3 x - 2 or 2 x 3} and its graphical representation is (c) P \ Q = { x : - 2 < x < 0} and its graphical representation is

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## This note was uploaded on 10/17/2011 for the course IELM 3010 taught by Professor Fugee during the Winter '11 term at HKUST.

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MS-Sol-EE-C12 - CHAPTER 12 PROBABILITY FUNDAMENTAL CONCEPTS EXERCISE 12.1 1 Section 12.1(page 159 Set notation D = cfw_a d e i m n r t n(D = 8(a E

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