For any two sets A and B, show that the following statements are equivalent:

Question

For any two sets A and B, show that the following statements are equivalent: A – B = ϕ

Philoid · Accepted Answer

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.