Q12 of 162 Page 1

For any two sets of A and B, prove that:

B’ ⊂ A’ A ⊂ B

We have B’⊂ A’


To Show: A ⊂ B


Let, x ϵ A


⇒ x∉ A’ [∵ A ∩ A’ = ϕ ]


⇒ x ∉ B’ [ ∵ B’ ⊂ A’ ]


⇒ x ϵ B [∵ B ∩ B’ = ϕ]


Thus, x ϵ A ⇒ x ϵ B


This is true for all x ϵ A


∴ A ⊂ B.


More from this chapter

All 162 →
11

Using properties of sets, show that for any two sets A and B, (A ∪ B) ∩ (A ∪ B’) = A.

 12

For any two sets of A and B, prove that:

A’ ∪ B = U A ⊂ B

 13

Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer.

 14

Show that for any sets A and B,

A = (A ∩ B) ∩ (A – B)