# Partial Ordering over a subset of a set

Given a partial ordering $R$ over a set $S$ is it true that for every $A\subseteq S$ that $R$ is also a partial ordering over $A$? I think so but I'm not sure.

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More precisely, $R\cap(A\times A)$ is a partial order on $A$. –  Brian M. Scott Feb 9 '12 at 8:51