For any two sets A and B, prove the following:
A – (A – B) = A ∩ B
For any sets A and B we have De morgans law
(A ∪B)’ =A’ ∩B’ , (A ∩ B)’ = A’ ∪ B’
=A – (A–B)
= A ∩ (A–B)’
= A∩(A∩B’)’
= A∩(A’∪ B’)’)
= A ∩ (A’∪B)
= (A ∩ A’) ∪ (A ∩ B)
= ϕ ∪ (A ∩ B)
= (A ∩ B)