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.