For any two sets A and B, prove the following:
A – B = A Δ (A ∩ B)
= A Δ (A ∩ B) [∵ E Δ F =(E–F) ∪ (F–E) ]
= (A–( A ∩ B)) ∪ (A ∩B –A) [∵ E – F = E ∩ F’]
= (A ∩ (A ∩ B)’) ∪ (A∩B∩A’)
= (A ∩ (A’∪B’)) ∪ (A∩A’∩B)
= ϕ ∪ (A ∩ B’) ∪ ϕ
= A ∩ B’ [∵A ∩ B’ = A–B]
= A–B
=LHS
∴ LHS=RHS Proved.