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

Example of differential equations, y(x) = x -3/2 is a solution to 4x 2 y′...

y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64 Solution :  As we noticed in previous illustration the function is a solution an

Find the value of x of eagle , A fox and an eagle lived at the top of a cli...

A fox and an eagle lived at the top of a cliff of height 6m, whose base was at a distance of 10m from a point A on the ground. The fox descends the cliff and went straight to the p

How many solutions are there for differential equation, If a differential e...

If a differential equation does have a solution how many solutions are there? As we will see ultimately, this is possible for a differential equation to contain more than one s

Stages of multiplication from the beginning, What is our aim when teaching ...

What is our aim when teaching children multiplication? Firstly they should be able to judge which situations they need to multiply in, and the numbers that are to be multiplied sec

Strategic , Hi need a help for marketing strategic assignment Could you ab...

Hi need a help for marketing strategic assignment Could you able to help me???

How many ounces of tomatoes does mark have, Mark has three 4 1/2 oz cans o...

Mark has three 4 1/2 oz cans of tomatoes and ?ve 8 1/4 oz cans. How many ounces of tomatoes does Mark have? Ignore the fractional parts of the mixed numbers at first and mul

Simpson rule - approximating definite integrals, Simpson's Rule - Approxima...

Simpson's Rule - Approximating Definite Integrals This is the last method we're going to take a look at and in this case we will once again divide up the interval [a, b] int

Theorem, #question if two angles of a triangle are unequal in measure then ...

#question if two angles of a triangle are unequal in measure then the side opposite to greater angle is longer than the side opposite to the smaller angle

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