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

Calculus, I need help with my calculus work

I need help with my calculus work

Solve 5x tan (8x ) =3x trig function, Solve 5x tan (8x ) =3x . Solution...

Solve 5x tan (8x ) =3x . Solution : Firstly, before we even begin solving we have to make one thing clear.  DO NOT CANCEL AN x FROM BOTH SIDES!!! Whereas this may appear like

What is the diameter of the pipe along with the insulation, A pipe has a di...

A pipe has a diameter of 2.5 inches. Insulation which is 0.5 inches thick is placed around the pipe. What is the diameter of the pipe along with the insulation around it? The i

Example of integration strategy - integration techniques, Evaluate the subs...

Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x)  dx Solution This kind of integral approximately falls into the form given in 3c.  It is a quotient of ta

Find the value of the derivative, Given y = f(x) = x 2 + 2x +3 a) Use the ...

Given y = f(x) = x 2 + 2x +3 a) Use the definitional formula given below to find the derivative of the function. b) Find the value of the derivative at x = 3.

Find the common difference & write the next 3 terms, If the following terms...

If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans:    d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,

Probablility, #question.find the number of combinations of the letters a, b...

#question.find the number of combinations of the letters a, b, c, and d taken 3 at a time.

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