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So I was assigned this problem for homework and I was able to all of them except for part D I would really appreciate any help or hintsenter image description here I have no clue where to start I looked through my book and everything anything would be appreciated

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1 Answer 1

We need to obtain a total ordering such that whenever $a < b$ in the partial ordering, we also have $a<b$ in this total ordering. Looking at the Hasse diagram, just pick out the minimal elements one by one. If there is more than one minimal element, pick any one arbitrarily. For example, first pick $e$ say, then $f, c,d,b,a$. This ordering $e<f<c<d<b<a$ is a total ordering compatible with the given partial ordering. Another order is $f,e,d,c,b,a$. In all cases, $e$ would be before $b$ and before $c$, $f$ would be before $c$ and before $d$, and $a$ would be last. This algorithm of removing minimal elements one by one is called topological sort.

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