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.’