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

History of Mathematics, What are the key features of Greek Mathematics? How...

What are the key features of Greek Mathematics? How does the emphasis on proof affect the development of Greek Mathematics?

Negative signs in fractions, Q. Negative Signs in Fractions? It reall...

Q. Negative Signs in Fractions? It really doesn't matter where you put a negative sign in a fraction.  The following are all the same: The negative sign can go in

Solve the fractional equation, Solve the fractional equation: Example...

Solve the fractional equation: Example: Solve the fractional equation 1/(x-2) +1/(x+3) =0 Solution: The LCD is (x - 2)(x + 3); therefore, multiply both sides of t

Find the area of the shaded region of square, In the adjoining figure, ABCD...

In the adjoining figure, ABCD is a square of side 6cm.  Find the area of the shaded region. Ans:    From P draw PQ ⊥ AB AQ = QB = 3cm (Ans: 34.428 sq cm) Join PB

Fractions, what Is the common denominator for 1/2 and 1/4

what Is the common denominator for 1/2 and 1/4

Math help, What fraction of the full price will you pay for 2 shirts? 3 4 ...

What fraction of the full price will you pay for 2 shirts? 3 4 11 2 $45.001 2 .

Sketch the plot first-order integrated rate, Show that the first-order inte...

Show that the first-order integrated rate expression can be written as [A] t = [A] 0 e -n(in)t where n represents the number of elapsed halftimes. Sketch the plot of [A] 1

Continuous Probability Distributions, Ask questioOn average, Josh makes thr...

Ask questioOn average, Josh makes three word-processing errors per page on the first draft of his reports for work. What is the probability that on the next page he will make a) 5

Determine the poisson probability distribution, A manufacturer assures his ...

A manufacturer assures his customers that the probability of having defective item is as 0.005. A sample of 1000 items was inspected. Determine the probabilities of having the give

External forces, It is the catch all force. If there are some other forces ...

It is the catch all force. If there are some other forces which we decide we need to act on our object we lump them in now and call this good. We classically call F(t) the forcing

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