= Solution
\b[No.] On $\{0,1,2\}$ take $R=\{(0,1),(1,2),(2,0)\}$. This is an <antisymmetric relation> because it contains no opposite pair of distinct elements. Its <reflexive transitive closure> contains every ordered pair: following the directed three-cycle reaches any vertex from any other. In particular it contains both $(0,1)$ and $(1,0)$, violating antisymmetry.
This illustrates the <reachability preorder>: collapsing mutually reachable vertices into <strongly connected components> yields a partial order, but retaining all original vertices need not.
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