Solution to Suppose S is a set containing 5 elements, and that ⪯ is a total ordering … - Sikademy
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Archangel Macsika

Suppose S is a set containing 5 elements, and that ⪯ is a total ordering of S. Draw the Hasse diagram for ⪯ (no need to label the vertices in your diagram).

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S=\{a,b,c,d,e\}

\preceq is a total order on S.

Any total order \preceq is reflexive, antisymmetric, transitive. Therefore (S,\preceq) form a poset.

Again as \preceq is a total order any two elements of S are comparable. Therefore

we can order the elements of S in such a way so that they form a chain

a\preceq b \preceq c\preceq d \preceq e (say).

The corresponding Hasse diagram is drawn in this convention using the undirected line, the \preceq relation (hence, the ordering of the elements) is read from the bottom up.


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