Explore BrainMass

Relations: reflexive, antisymmetric, transitive

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R:


Row 1: 1 0 1

Row 2: 1 1 0

Row 3: 0 1 1


Which of the properties (reflexive, antisymmetric, transitive) are satisfied by R?

Begin your discussion by defining each property in general, and then determine whether R satisfies that property.

© BrainMass Inc. brainmass.com October 24, 2018, 9:27 pm ad1c9bdddf


Solution Preview

We use the positions of the 1's in the matrix M_R to determine R (i.e., to determine the set of ordered pairs of elements of the set {a, b, c} which belong to R):

From the first row of M_R (which indicates the elements (a, x) in R, for x in A), we see that (a, a) and (a, c) are in R (but not (a, b)), because the first and third elements of the first row are the locations of the 1's.

From the second row of M_R (which indicates the elements (b, x) in R, for x in A), we see that (b, a) and (b, b) are in R (but not (b, c)), because the first and second elements of the second row are the locations of ...

Solution Summary

Definitions are given of the following properties of a binary relation: reflexive, antisymmetric, and transitive. A detailed determination of which of these are properties of the given relation is presented.

See Also This Related BrainMass Solution

Reflexive, Antisymmetric and Transitive Properties

Please see the attached file for the fully formatted problems.

Let A = {1, 2, 3, 4, 5, 6,12} and define the relation R on A by m R n iff
Write the definitions of the properties, reflexive, antisymmetric and transitive and the use
the definitions to determine whether each property holds for this relation.

(a) Is this relation a partial ordering relation? Why? If so, draw its Hasse

(b)Write the (boolean, that is the yes/no) matrix of this relation.

View Full Posting Details