For any two sets A and B, prove that: A’ – B’ = B – A

Question

Philoid · Accepted Answer

To show, A’ – B’ = B – A

We need to show

A’ – B’ ⊆ B – A

B – A ⊆ A’ – B’

Let, x ϵ A’ – B.’

⇒ x ϵ A’ and x ∉ B.’

⇒ x ∉ A and x ϵ B

⇒ x ϵ B – A

It is true for all x x ϵ A’ – B’

∴ A’ – B’ = B – A

Hence Proved.