Q3 of 162 Page 1

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

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


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A ∩ (A ∪ B’) = ϕ

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A – B = A Δ (A ∩ B)

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(A ∪ B) – B = A – B

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