Hasse diagram: minimal, least, greatest

Let S = {2,3,4,5} and consider the poset (S, <=) where <= is the divisibility relation. Which of the following is true?

1. 3 is a minimal element

2. 4 is a greatest element

3. 2 is a least element

4. Both 2 and 3

My answer: 1

In a Hasse diagram 3 and 5 are not connected to anything, and I'm unsure if this affects the answer. Suggestions?

Re: Hasse diagram: minimal, least, greatest

Quote:

Originally Posted by

**nicnicman** My answer: 1

You are right. Other minimal elements are 2 and 5. Also, 3, 4 and 5 are maximal elements. There are no least or greatest elements.

Re: Hasse diagram: minimal, least, greatest

Yeah, that's what I thought. I just didn't know if there was some stipulation if the elements are not connected to other elements.

Thank you.