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?

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

... for (a) Describe R by listing the ordered pairs in R ... If this relation is a partial order, draw its ... detailed steps on solving a couple of discrete questions. ...

... Answer For this question keep this with you always, the equation of ... 17-----Write a formula that expresses the relationship described by each ...

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...QUESTIONS 9. ... coefficient, r So the first step to answer this question it so ... above the critical value (-1.9 is larger then -1.6), the relationship is significant ...

... Q 12 The question is incomplete. ... Q2 The relation is not a function ... Last two ordered pairs, (- 1, - 2) and ( - 1, 7) have same first element : - 1. Therefore the ...

Two questions in group theory. Problem ... thus . Thus xy satisfy all the generator relations for . ... have . The only groups of order 6 are and . ...

... Set 3 #34 Function expressed by ordered pairs: determine whether each relation is a function [(2, -5), (2,5) (3, 10)] In this question, for a given value x of 2 ...

... mathch5) that we can use and the actual questions are from ... 5.1 Relations Deﬁnition 16 Let S be a set ... Two ordered pairs, (x, y ) and (u, v ) are equal means x ...