For any two sets A and B, show that the following statements are equivalent:
A – B = ϕ
We need to show that 2 ⇒ 3
So assume that A–B = ϕ
To show: A∪B = B.
∵ A – B = ϕ
∴ Every element of A is an element of B.
So A ⊂ B and therefore A∪B = B
So (2) ⇒ (3) is true.