draw the directed graph of the reflexive closure of the relations with the directed graph shown
The reflexive closure is given by the relation plus all the directed edges are needed to make the new relation reflexive. Hence we add the loops on $b$, $c$, and $d$ and obtain the following:
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The reflexive closure is given by the relation plus all the directed edges are needed to make the new relation reflexive. Hence we add the loops on $b$, $c$, and $d$ and obtain the following: