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

#title.simpal harmonic motion., #questionShow that the system oscillates in...

#questionShow that the system oscillates in simple harmonic motion demonstrated by; , for which the general solution where X = (x – x0)..

Percent problems.., I have a graph, i need to determine the many hours per ...

I have a graph, i need to determine the many hours per day becky spends on math activity if she does it 25% of her day.

Marketing., what is product life cycle

what is product life cycle

What is the probability shane rolls a 5, Shane rolls a die numbered 1 by 6....

Shane rolls a die numbered 1 by 6. What is the probability Shane rolls a 5? From 2:15 P.M. to 4:15 P.M. is 2 hours. After that, from 4:15 P.M. to 4:45 P.M. is another half hour

Laws of set algebra, Laws of Set Algebra From the given Venn diagram w...

Laws of Set Algebra From the given Venn diagram where T is the universal set and A its subset that we can deduce a number of laws as: i. A υ Ø = A ii. A υ T = T

What is his test average, Steve earned a 96 percent on his ?rst math test, ...

Steve earned a 96 percent on his ?rst math test, a 74% on his second test, and an 85 percent on his third test. What is his test average? Add the test grades (96 + 74 + 85 = 25

Nine minus five times a number, Nine minus five times a number, x, is no le...

Nine minus five times a number, x, is no less than 39. Which of the subsequent expressions represents all the possible values of the number? Translate the sentence, "Nine minus

Mode, how to work out mode

how to work out mode

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