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

Find out the area under the parametric curve, Find out the area under the p...

Find out the area under the parametric curve given by the following parametric equations.  x = 6 (θ - sin θ) y = 6 (1 - cos θ) 0 ≤ θ ≤ 2Π Solution Firstly, notice th

If 967.234 is divided by 10 how will the decimal point move, If 967.234 is ...

If 967.234 is divided by 10, how will the decimal point move? It will move one place to the left. While dividing by multiples of 10, the decimal point is moved to the left acco

Determine if r is equivalence relation or a partial ordering, Let R be the ...

Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc.  Determine whether R is an equivalence relation or a p

Determine the average bit rate - huffman codebook, 1. Consider a source wi...

1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.

Probability rules, Probability Rules A probability is a number as...

Probability Rules A probability is a number assigned to the occurrence of an event in a sample space. Probability measures must satisfy three rules. If A is an even

Conclude the values of the six trigonometric functions, Conclude the values...

Conclude the values of the six trigonometric functions: Conclude the values of the six trigonometric functions of an angle formed through the x-axis and a line connecting the

Cynthia, #stioquen..Store A is advertising a sale that will reduce prices o...

#stioquen..Store A is advertising a sale that will reduce prices on all merchandise by 15%. Store B is advertising a sale that will reduce prices on all merchandise by one over fiv

Explain multiplying-dividing negative fractions, Explain Multiplying/Dividi...

Explain Multiplying/Dividing Negative Fractions? There are 3 steps to multiplying or dividing fractions. 1. If any negative signs are present, place them next to the numerator

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