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

Statistics, How do I choose a distribution test for a sample size of 60? Pr...

How do I choose a distribution test for a sample size of 60? Probability of rolling a 4 on a six sided die.

Find the maxima and minima - equal pi, 1) Find the maxima and minima of f(x...

1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving

Compositions of relations, Let Consider R A Χ B, S B Χ C be two relation...

Let Consider R A Χ B, S B Χ C be two relations. Then compositions of the relations S and R given by SoR A Χ C and is explained by (a, c) €(S o R) iff € b € B like (a, b) € R,

Types of infinity, TYPES OF INFINITY : Mostly the students have run across...

TYPES OF INFINITY : Mostly the students have run across infinity at several points in previous time to a calculus class. Though, when they have dealt along with this, this was jus

How to convert decimals to fractions, Q. How to Convert decimals to fractio...

Q. How to Convert decimals to fractions? Ans. Note: This tutorial covers only terminating decimals.

What is the limit of sin (1/x) when x tends to zero?, As x tends to zero th...

As x tends to zero the value of 1/x tends to either ∞ or -∞. In this situation we will not be sure about the exact value of 1/x. As a result we will not be sure about the exact/app

What is the formula to know total area square shaped quilt, Cathy is formin...

Cathy is forming a quilt out of fabric panels that are 6 in through 6 in. She needs to know the total area of her square-shaped quilt. Which formula will she use? The area of a

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