For any sets A,&B and,

using properties of sets prove that :

A-(AnB)=A-B;

A – (A ∩ B) = A ∩ (A ∩ B)′ (since A – B = A ∩ B′)
= A ∩ (A′ ∪ B′) [by De Morgan’s law)
= (A ∩ A′) ∪ (A ∩ B′) [by distributive law]
= φ ∪ (A ∩ B′)
= A ∩ B′ = A – B