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 = B

Philoid · Accepted Answer

We need to show that 3 ⇒ 4

Assume that A ∪ B = B

To show: A ∩ B = A.

∵A ∪ B = B

∴ A⊂ B and so A ∩ B = A.

So (3) ⇒ (4) is true.