Q about equivalence relations

[j0hnnyb0y84]

Hey all,

Just trying out the forums, since I can't seem to think up a proof/answer for this problem:

Let S be a set with 5 elements. How many equivalence relations are there on S?

I'm having a hard time starting out the problem. We've been discussing partitions and such in class, so I'd like to think it's related to this. One of the other proofs I'm having difficulty with is:

Summarize the existence part of the Proof of Division Algorithm (less than 50 words).

I've got a start on it because he gave us a couple of hints in class, but my knowledge is somewhat limited - could someone enlighten me?

Thank you,

Johnny

 

[pka]

Each equivalence relation on a non-empty set determines a partition of the set:
Elements that are equivalent belong to the same cell.

Every partition determines an equivalence relation:
All equivalent elements form a cell in the partition.