Need help understanding Posets

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1. The problem statement, all variables and given/known data
I don't really have a specific problem here except that I just don't really get the base ideas for Posets. I know that if someone could explain them to me "Barney" style, I would be good on the more advanced ideas. Any help is appreciated.


2. Relevant equations
Specifically, I am looking for explanations of what a chain and antichain are. Also with the idea of elements being comparable and incomparable.



3. The attempt at a solution
I know that when x and y are distinct points and either x ≤ y in P or y ≤ x in P, we say x and y are comparable; else they are incomparable (not comparable). I also know that a subset C is called a chain when every pair of points in C is a comparable pair. I just don't understand fully what these two statements are saying.
 

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