Q6 of 162 Page 1

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

A ⊂ B C – B ⊂ C – A

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.


More from this chapter

All 162 →
5

For any two sets A and B, show that the following statements are equivalent:

A ∩ B = A.

 6

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

A ∩ B = A ∩ C need not imply B = C.

 7

For any two sets, prove that:

A ∪ (A ∩ B) = A

 7

For any two sets, prove that:

A ∩ (A ∪ B) = A