Let A = {a, b, c} , and let R be the relation defined on A defined by the following matrix:?

MR = 1 0 1


1 1 0


0 1 1





(a) (10 pts.) Describe R by listing the ordered pairs in R and draw the digraph of this relation.





(b) (15 pts.) 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) (5 pts.) Is this relation a partial order? Explain. If this relation a partial order, draw its Hasse diagram.


(d) (10 pts.) Use Warshall’s Algorithm (Section 8.4 of the text.) to determine the transitive closure of R. Note there are 2 versions of Washall’s Algorithm given in the text, that illustrated by example 7, page 549 and that illustrated by example 8, page 551. Use any version you wish.


(e) (5 points) 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?

Let A = {a, b, c} , and let R be the relation defined on A defined by the following matrix:?
MR = 1 0 1


1 1 0


0 1 1





(a) (10 pts.) Describe R by listing the ordered pairs in R and draw the digraph of this relation.





(a,a), (a,b), (b,b), (b,c), (c,a), (c,b) .

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