Nested Familiy

[Willy_Will]

Hi all,

Im having trouble with this problem, I dont know where to begin.

Suppose that Ä is a nested family of sets.

1. Prove that U (from k=1 to infite) A(sub k) = A(sub l)

2. Prove that ∩ (from k=1 to n) A(sub k) = A(sub n)


Thanks in advace mathematicians!

-William

 

[ZioX]

1) To show that they are equal you must show that they are subsets of one another.

2) If x is in the union of a collection of sets, what does this mean?

3) If x is in the intersection of a collection of sets, what does this mean?

4) You have to use the assumption of nested somewhere.

5) If A is a subset of B what can you say about A n b?

6) If A is a subset of B what can you say about A U B?