Nested Familiy

  • Thread starter Willy_Will
  • Start date
  • #1
15
0
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
 

Answers and Replies

  • #2
370
0
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?
 

Related Threads on Nested Familiy

  • Last Post
Replies
2
Views
547
  • Last Post
Replies
5
Views
725
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
2
Views
2K
Top