For any two sets of A and B, prove that: A’ ∪ B = U A ⊂ B

Question

Philoid · Accepted Answer

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