Elements and sets

Question

A. List the elements of each of the following (roster method). Use '...' notation for infinite sets
B = {x : x is an integer -3 < x < 4}
B = {x : x is a positive integer and multiple of three}
B = {x : (3x-1)(x+2) = 0}
B = {x : 2x and x are integers}

 

B. Let U = {1,2,3, ...9,10} 

A = {2,4,6,8,10}

B = {3,4,5,6}

C = {7,8,9,10}

D = {1,3,5,7,9}

1) (A' union B') - (A union B)'

2) (C' - A) intersect (A - C')

Answer 1

{x l x is an integer and -3 < x < 4} = {-2, -1, 0, 1, 2, 3}

 

{x l x is a positive integer and x is a multiple of 3} = {3, 6, 9,...}

 

{x l (3x-1)(x+2)=0} = {1/3, -2}

 

{x l 2x and x are integers} = {0, ±1, ±2, ±3,...}

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A' = {1, 3, 5, 7, 9}   B' = {1, 2, 7, 8, 9, 10}

 

      A' υ B' = {1, 2, 3, 5, 7, 8, 9, 10}

 

      A υ B = {2, 3, 4, 5, 6, 8, 10} So, (A υ B)' = {1, 7, 9}

 

(A' υ B') - (A υ B)' = {2, 3, 5, 8 ,10}

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C' = {1, 2, 3, 4, 5, 6}

 

C' - A = {1, 3, 5}

 

A - C' = {8, 10}

 

(C' - A) ∩ (A - C') = Ø

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Answer 2

B = {x : x is an integer -3 < x < 4}                             :B={-2,-1,0,1,2,3}
B = {x : x is a positive integer and multiple of three}    :B={3,6,9,..........}

B = {x : (3x-1)(x+2) = 0}                                          :B={1/3,-2}
B = {x : 2x and x are integers}                                   :B=

B. Let U = {1,2,3, ...9,10}
A = {2,4,6,8,10}
B = {3,4,5,6}
C = {7,8,9,10}
D = {1,3,5,7,9}
1) (A' union B') - (A union B)'    

    

A'={1,3,5,7,9}       [As A'= U-A]

B'={1,2,7,8,9,10}   [As B'= U-B]

A' union B'={1,2,3,5,7,8,9,10}

A union B ={2,3,4,5,6,8,10}

(A union B)' ={1,7,9}

 

So (A' union B') - (A union B)'  ={2,3,5,8,10}

 

2) (C' - A) intersect (A - C')   

In similar manner solve this part also