Question: For all sets A and B, A – (A ∩ B) is equal to ____________.
Solution:
For set A and B
A – (A ∩ B) = A ∩ (A ∩ B)' (By defination of A – B)
= A ∩ (A' ⋃ B') (By De-Morgan's law)
= (A ∩ A') ⋃ (A ∩ B') (By Distributive law)
= ϕ ⋃ (A ∩ B')
= A ∩ B'
i.e A – (A ∩ B) = A – B
