I Let A = {1,2,3,4,5,6.} # of many different relations possible

1. Nov 21, 2016

Logical Dog

How many different relations are possible? Is the question.

Is the answer the power set of AxA?
2^36.

2. Nov 21, 2016

Staff: Mentor

Yes.

3. Nov 21, 2016

Logical Dog

I do not understand this too. I am getting an empty set for it.

4. Nov 21, 2016

Staff: Mentor

No, not an empty set, because everything is related to everything without itself. The main diagonal is missing. But I cannot think of a familiar relation.
Something like: every hand can wash every hand, but not itself. However, what is this mathematically?

Edit: e.g. the domain of $(x,y) \longmapsto (x-y)^{-1}$.

Last edited: Nov 21, 2016
5. Nov 21, 2016

jbriggs444

This follow-up question appears to be homework, so I do not want to blurt out what seems to be the expected answer.

6. Nov 21, 2016

Staff: Mentor

Got it.

7. Nov 21, 2016

Logical Dog

no not homework just personal reading. :) I was going over relations once more as I never got it completely the first time. It is a question in this book (and I just noticed that it has solutions there too but they are only for ODD numbered questions
http://www.people.vcu.edu/~rhammack/BookOfProof/

8. Nov 21, 2016

jbriggs444

The difficulty is that the the "homework" umbrella on these forums encompasses both material that is actual homework and material that is homework-like, even though it may not be an assigned homework problem in a course that is currently being taken.

See the sticky posting at the top of this forum: https://www.physicsforums.com/threa...mework-or-any-textbook-style-questions.42532/

9. Nov 21, 2016

Staff: Mentor

As jbriggs444 said, your post falls under the heading of "homework," which includes problems from books even if you are not in a course that uses that textbook.