For any two sets of A and B, prove that:

B’ ⊂ A’ A ⊂ B

We have B’⊂ A’

To Show: A ⊂ B

Let, x ϵ A

⇒ x∉ A’ [∵ A ∩ A’ = ϕ ]

⇒ x ∉ B’ [ ∵ B’ ⊂ A’ ]

⇒ x ϵ B [∵ B ∩ B’ = ϕ]

Thus, x ϵ A ⇒ x ϵ B

This is true for all x ϵ A

∴ A ⊂ B.