If A, B, C are three sets such that A ⊂ B, then prove that C – B ⊂ C – A.

Question

Philoid · Accepted Answer

We have, ACB.

To show: C – B ⊂ C – A

Let, x ϵ C–B

⇒ x ϵ C and x∉ B

⇒ x ϵ C and x∉ A

⇒ x ϵ C – A

Thus, x ϵ C–B ⇒ x ϵ C – A

This is true for all x ϵ C–B

∴ C – B ⊂ C – A