For any two sets of A and B, prove that:
A’ ∪ B = U A ⊂ B
To show: A⊂B
⇒ x ∉ A
⇒ x ϵ A and A ⊂ U
⇒ x ϵ A
⇒ x ϵ (A’ ∪ B) [∵ U = A’∪ B]
⇒ x ϵ A’ or x ϵ B
But, x ∉ A’,
∴ x ϵ B
Thus, x ϵ A ⇒ x ϵ B
This is true for all x ϵ A
∴ A ⊂ B