Question: Prove the following. Let R be a partial order on the set X. Let A be an antichain with ||2|A|2. If xA, then x is

Prove the following.

Let R be a partial order on the set X. Let A be an antichain with ||2|A|2. If xA, then x is not a greatest element.

(Recall that in a poset (,)(X,R), a set of pairwise incomparable elements of X is called an antichain.)

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