Question
Find the directed graphs of the symmetric closures of the relations with directed graphs shown in Exercises 5–7.
Step 1
The symmetric closure of a relation R on a set A is the smallest symmetric relation on A that contains R. In terms of directed graphs, this means that for every directed edge from a vertex A to a vertex B, there should be a corresponding directed edge from B to A. Show more…
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Find the directed graph of the smallest relation that is both reflexive and symmetric that contains each of the relations with directed graphs shown in Exercises 5–7.
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Closures of Relations
In Exercises 5–7 draw the directed graph of the reflexive closure of the relations with the directed graph shown.
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