Let ≤ be a reflexive, antisymmetric relation on a finite set A. Show that this relation can be extended to an appropriate finite superset B of A such that ≤ on B remains reflexive, antisymmetric, and any two elements of B have a least upper bound as well as a greatest lower bound. (The relation ≤ is extended to B if for x,y∈A,x≤y holds in A if and only if it holds in B.)
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