Question

If A = {1,3 ,5 ,7 ,9 ,11 ,13 ,15 ,17}

B = {2 ,4 ,6 ,8 ,10 ,12 ,14 ,16 ,18) 

U = {1 ,2 ,3 , … . .}

And U is universal set then find A' ∪ [(A∪B) ∩ B]

Answer 1

Given, A = {1 ,3 ,5 ,7 ,9 ,11 ,13 ,15 ,17} 

i.e. A = {x ∶ x is an odd number; 1 ≤ x ≤ 18}  

And B = {2 ,4 ,6 ,8 ,10 ,12 ,14 ,16 ,18} 

i.e. B = {x ∶ x is an even number; 1 ≤ x ≤ 18} 

Now, A’ = {x ∶ x is an even number; 1 ≤ x ≤ 18} 

= {2 ,4 ,6 ,8 ,10 ,12 ,14 ,16 ,18}= B 

And B' {x ∶ x is an odd number; 1 ≤ x ≤ 18} 

= {1,3,5,7,9,11,13,15,17} = A

(A∪B) = {1,3,5,7,9,11,13,15,17} ∪ {2,4,6,8,10,12,14,16,18} = {1, 2, 3, 4,….18} 

(A∪B) ∩ B’ = {1, 2, 3, 4,….18} ∩ {1,3,5,7,9,11,13,15,17} = (1,3,5,7,9,11,13,15,17) 

A’ ∪ {(A∪B)} ∩ B’} = {2,4,6,8,10,12,14,16,18} ∪ {1,3,5,7,9,11,13,15,17} = {1, 2, 3, ….18}