Prove that A – B = A ∩ B.’

Let x be some element in set A – B that is x ∈ (A – B)

Now if we prove that x ∈ (A ∩ B’) then (A – B) = (A ∩ B’)

x ∈ (A – B) means x ∈ A and x ∉ B

Now x ∉ B means x ∈ B.’

Hence we can say that x ∈ A and x ∈ B.’

Hence x ∈ A ∩ B.’

And as x ∈ A ∩ B’ and also x ∈ A – B we can conclude that

A – B = A ∩ B.’