0
$\begingroup$

The question I have problem with is

a) How many partial orders for the set {x,y} has x as a minimal element

b) How many partial orders for the set {x,y,z} has x as a minimal element

I don't really get how I should think. I believe I understand how it works when you use a diagram, but now I can't get a grip on how the diagram would look for a problem like this. Or can't you use that way of thinking in this problem?

$\endgroup$
1
$\begingroup$

a. There are three orders for {x,y}, x < y, y < x and
{x,y} is an antichain (x and y cannot be compared, x||y).
Which of those orders have x as a minimal order?

b. What are the possible orders for {x,y,z}?
If you must have diagrams, then draw a diagram for each order.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.