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dia

I think I know the answer but I am not quite sure.

Any help would be much appreciated.

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  • $\begingroup$ What do you think is the answer? $\endgroup$ Aug 20, 2019 at 19:10
  • $\begingroup$ I will try to describe it as I don't know any other way of showing you (not used to this site much). $\endgroup$ Aug 20, 2019 at 19:11
  • $\begingroup$ a------c whilst also having b-----d-----c, if you get me? $\endgroup$ Aug 20, 2019 at 19:11

1 Answer 1

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Think: Transitive reduction ... https://en.wikipedia.org/wiki/Hasse_diagram enter image description here

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  • $\begingroup$ Just to check, does that make the minimal element(s) B rather the minimal element(s) being A and B? My question more being: what makes B a minimal element (if it is) as opposed to A and B being on the same level? Is it simply because B has a longer order/partially ordered to more elements? $\endgroup$ Aug 20, 2019 at 19:23
  • $\begingroup$ If I were to refer to {a,b} as a pair, would that make sense? Because aren't pairs meant to be on the same level? $\endgroup$ Aug 20, 2019 at 19:26
  • $\begingroup$ $a$ and $b$ are maximal elements (assuming your arrows are that way up?). "at the same level" becomes dubious in some larger posets. Have a look at the example in wiki en.wikipedia.org/wiki/Hasse_diagram#A_%22good%22_Hasse_diagram $\endgroup$ Aug 20, 2019 at 19:38
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    $\begingroup$ It's important to understand that a and b are not comparable in this partial order. There is no reasonable way to evaluate them being "on the same level" $\endgroup$
    – user694818
    Aug 20, 2019 at 20:02
  • $\begingroup$ To emphasize the last point: One could move A so that it was on the same 'level' as B, and it would still be a valid Hasse diagram. What matters is its structure as a directed graph, not the particular placement of nodes. $\endgroup$ Aug 20, 2019 at 20:46

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