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

Philoid · Accepted Answer

To show that the following four statements are equivalent, we need to show that 1⇒2, 2⇒3, 3⇒ 4, 4⇒1

We first show that 1⇒ 2

Now A–B = {xϵ A: x ∉ B} .As A ⊂ B,

∴ Each element of A is an element of B,

∴ A–B = ϕ

Hence we proved 1⇒ 2.