Determine the relation is partially ordered, Mathematics

Assignment Help:

Determine if the relation represented by the following Boolean matrix is partially ordered.

133_Determine the relation is partially ordered.png

Ans: Let the following relation R is defined on set A = {x, y, z}. To test if the relation R is partially ordered, we have to test if R is reflexive, anti symmetric and transitive.   

Reflexivity: As all elements in the principal diagonal is '1', R is reflexive.  

Anti Symmetry: In the following relation, we do not comprise any pairs (x, y) & (y, x) like that x ≠ y that is for (x, y) & (y, x) in R, x = y.  So R is anti symmetric.  

Transitivity: The relation is not transitive since for (y, x) & (x, z) in R, (y, z) is not in R.  Hence R is not partially ordered.


Related Discussions:- Determine the relation is partially ordered

Trigonometry, explain the formular for finding trigonometry

explain the formular for finding trigonometry

Find where the breakdown occurred and his original speed, A cyclist, after ...

A cyclist, after riding a certain distance, stopped for half an hour to repair his bicycle, after which he completes the whole journey of 30km at half speed in 5 hours.  If the bre

Terminology related to division, Terminology related to division :   A goo...

Terminology related to division :   A good way to remedy this situation is to familiarise children with these concepts in concrete, contexts, to start with. For instance, if a chi

Multiplication of complex numbers, Multiplication of complex numbers Af...

Multiplication of complex numbers After that, let's take a look at multiplication.  Again, along with one small difference, it's possibly easiest to just think of the complex n

Comperative statics, Discuss comparative statics,Market model and Nationa i...

Discuss comparative statics,Market model and Nationa income model

Chain rule, Chain Rule :   If f(x) and g(x) are both differentiable func...

Chain Rule :   If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x).  Proof We will s

Probability, Probability -Probability is an extremely popular concept ...

Probability -Probability is an extremely popular concept in business management. Since it covers the risks such may be included in certain business situations. This is a fact

Conscious consumer, a group of 3o students is planning a thanksgiving party...

a group of 3o students is planning a thanksgiving party items needed hats @ $2.50 each.noise makers@$4.00 per pack of 5.Ballons @$5.00 per pack of 10.how many packs of noisemakers

Learn, how to find basic intrest problems

how to find basic intrest problems

Communicating the meaning of addition, COMMUNICATING THE MEANING OF ADDITIO...

COMMUNICATING THE MEANING OF ADDITION :  One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and on

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd