# Set Theory

1. Sep 19, 2005

### nishap

Hi All

I have a problem with Set theory. I am given to prove the following;

Is the intersection of two equivalence relations itself an equivalance relation? If so , how would you characterize the equivalnce sets of the intersection?

Regards,
Nisha.

2. Sep 19, 2005

### Tom Mattson

Staff Emeritus
Hi Nisha,

We have a policy here which is posted at the top of this Forum. In order to receive help, you have to show us how you started and where you got stuck.

3. Sep 19, 2005

### George Jones

Staff Emeritus
For any sets A and B, a (binary) relation from A to B is a subset of AxB.

Of what set is an equivalence relation a subset?

What conditions must this subset satisfy?

Since equivalence relations are (sub)sets, the intersection of 2 equivalence relations is a set. Does this set satisfy the conditions required of an equivalence relation?

Regards,
George

4. Sep 19, 2005

### NateTG

Just in case you have no clue where to start - going back to the definitions is very helpful.