If A = 2 , 3 , 5 , 7 , 8 , B = 1 , 5 , 9 and A ' = 1 , 4 , 6 , 9 , verify that A ∪ B ' = A ' ∩ B ' .

Given A = 2 , 3 , 5 , 7 , 8 , B = 1 , 5 , 9 and A ' = 1 , 4 , 6 , 9 ∴ S = A ∪ A ' = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } Union of two given sets is the smallest set which contains all the elements of both the sets. ⇒ A ∪ B = 1 , 2 , 3 , 5 , 7 , 8 , 9 Complement set: All elements (from a Universal set) not in our set. ⇒ A ∪ B ' = 4 , 6 and B ' = 2 , 3 , 4 , 6 , 7 , 8 Now, A ' ∩ B ' = 4 , 6 ∴ A ∪ B ' = A ' ∩ B '

If A = 2 , 3 , 5 , 7 , 8 , B = 1 , 5 , 9 and A ' = 1 , 4 , 6 , 9 , verify that B - A = A ' ∩ B .

Given that A = 2 , 3 , 5 , 7 , 8 , B = 1 , 5 , 9 and A ' = 1 , 4 , 6 , 9 The difference of two sets written by B - A is the set of all elements of B which are not present in A . So, we have B - A = 1 , 9 . . . { 1 } The intersection contains the elements that the two sets have in common. ⇒ A ' ∩ B = 1 , 9 . . . ( 2 ) From ( 1 ) and ( 2 ) , we get B - A = A ' ∩ B