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Question -

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



Answer -

Given, ACB
To prove: C – B ⊂ C – A
Let us consider, x ∈ C–B
⇒ x ∈ C and x ∉ B
⇒ x ∈ C and x ∉ A
⇒ x ∈ C – A
Thus, x ∈ C–B ⇒ x ∈ C – A
This is true for all x ∈ C–B
∴ C – B ⊂ C – A
Hence proved.

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