Question

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

A ⊂ B

Answer 1

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.