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Question about Relation - Ordered Pairs

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5. Let A = {a, b, c} , and let R be the relation defined on A by the following matrix:
MR =
(a) Describe R by listing the ordered pairs in R and draw the digraph of this relation.

(b) Which of the properties: reflexive, antisymmetric and transitive are true for the given relation? Begin your discussion by defining each term in general first and then how the definition relates to this specific example.
(c) Is this relation a partial order? Explain. If this relation a partial order, draw its Hasse diagram.
(d) Use Warshall's Algorithm to determine the transitive closure of R. Note there are 2 versions of Washall's Algorithm. Use any version you wish.
(e) Draw the digraph of the transitive closure of R and use the digraph to explain the idea of connectivity. Is this graph connected? What does connectivity mean?

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This provides examples of answering questions about a relation, including ordered pairs, digraphs, properties, Wasrshall's algorithm, and partial order.

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