Question

If A = {1, 2, 3, B = {2, 3, 4}, C = {3, 4, 5, 6} and U = {1, 2, 3, 4, 5, 6, 7}. Find 

(i) (A ∪ B)’ 

(ii) Verity (A ∩ B)’ = A’ ∪ B’

Answer 1

(i) A ∪ B = {1,2, 3, 4} 

∴ (A ∪ B)’ = ∪ – (A ∪ B) = {5, 6, 7} 

(ii) (A ∩ B) = {2,3} 

(A ∩ B)’ = ∪ – (A ∩ B) = {1,4, 5,6} …… (1) 

⇒ A’ = ∪ – A = {4, 5, 6, 7} 

B’ = ∪ – B = {1, 5, 6, 7} 

∴ A’ ∪ B’ = (1,4, 5, 6, 7} ……. (2) 

From (1) and (2) (A ∩ B)’ = A’ ∪ B’