1.

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

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



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