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

Statewide mortality rates, Assume that between workers exposed to asbestos ...

Assume that between workers exposed to asbestos in a shipyard in 1980, 33 died over a 10 year period from COPD, whereas only 24 such deaths would be expected based on statewide mor

Angles, samuel left mauritius at 22:30 on saturday and travelled to london ...

samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min

Estimates the probabilities of price changes, Mr. Hoper is in charge of inv...

Mr. Hoper is in charge of investments for the golden horizon company. He estimates from past price fluctuations in the gold market that the probabilities of price changes on a give

Math, how do you add all the Y.AND X UP WITH 3

how do you add all the Y.AND X UP WITH 3

Example of union of sets, Need help, please anybody solve this: Consider...

Need help, please anybody solve this: Consider the universal set T and its subsets A, B and C underneath as: T = {a, b, c, d e, f} A = {a, d} B = {b, c, f} C = {a, c

Properties of radicals, If n is positive integer greater than 1 and a & b b...

If n is positive integer greater than 1 and a & b both are positive real numbers then, Consider that on occasion we can let a or b to be negative and yet have these propert

Analysis of algorithm running time - undirected graph, Problem. You are giv...

Problem. You are given an undirected graph G = (V,E) in which the edge weights are highly restricted. In particular, each edge has a positive integer weight of either {1, 2, . .

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