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.

Question about Ordered Pairs. ... The questions about ordered pairs are determined. Let A = {a, b, c} , and let R be the relation defined on A defined by the ...

... 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. ...

... H 0 : ρ = 0 . So we conclude that there is No significant linear relationship between x and y. Question 3 Given the following ordered data pairs (x, y ...

... The response was given a rating of "5/5" by the student who originally posted the question. ...Relation: A relation is simply a set of ordered pairs. ...

... This posting explains some questions on binary relations(reflexive ... D = {3, 4} and define a binary relation S from C ... y. ⇔ a) Write S as a set of ordered pairs. ...

...Question 2. ... keys, and also discusses the requirements needed for a two dimensional table in order to be a relation. References are provided for both questions. ...

Math problems. ... We will have the following ordered pairs: x Y. -4 -5. -2 -4. ... Exercise 3.5. 6. Since the relationship is directly proportional, we will have: m∝ p. ...

...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 ...