If A = {4, 6, 7, 8, 9} , B = {2, 4, 6} and C = {1, 2, 3, 4, 5, 6}, then find (i) A U (B ∩ C) (ii) A ∩ (B U C) (iii) A \ (C \ B)

Question 4 :
If A = {4, 6, 7, 8, 9} , B = {2, 4, 6} and C = {1, 2, 3, 4, 5, 6}, then find
(i) A U (B ∩ C) (ii) A ∩ (B U C)    (iii) A \ (C \ B)
Solution :
(i) A U (B ∩ C)
(B ∩ C) = {2, 4, 6} ∩ {1, 2, 3, 4, 5, 6}
 = {2, 4, 6}
A U (B ∩ C) = {4, 6, 7, 8, 9} U {2, 4, 6}
 = {2, 4, 6, 7, 8, 9}
(ii) A ∩ (B U C)
(B U C) = {2 ,4, 6} U {1, 2, 3, 4, 5, 6}
       = {1, 2, 3, 4, 5, 6}
A ∩ (B U C) = {4, 6, 7, 8, 9} ∩ {1, 2, 3, 4, 5, 6}
            = {4, 6}
(iii) A \ (C \ B)
C \ B = {1, 2, 3, 4, 5, 6} \ {2, 4, 6}
    = {1, 3, 5}
A \ (C \ B) = {4, 6, 7, 8, 9} \ {1, 3, 5}

           = {4, 6, 7, 8, 9}