For three sets A, B, and C, show that A ⊂ B C – B ⊂ C – A

Question

Philoid · Accepted Answer

Given: A ⊂ B

To show: C–B ⊂ C–A

Let x ϵ C– B

⇒ x ϵ C and x ∉ B [by definition C–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.