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

Absolute mean deviation-measures of central tendency, Illustration 1 I...

Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60

Childrens errors are a natural and inevitable part, Childrens errors are a ...

Childrens errors are a natural and inevitable part of their process of learning. In the process of grasping new concepts, children apply their existing understanding, which may

Round 14.851 to the nearest tenth, Round 14.851 to the nearest tenth? T...

Round 14.851 to the nearest tenth? The tenths place is the ?rst number to the right of the decimal. Here the number 8 is in the tenths place. To decide whether to round up or

Circumference of a circle, How far will a bowling ball goes in one rotation...

How far will a bowling ball goes in one rotation if the ball has a diameter of 10 inches? (π = 3.14) 1. 78.5 in 2. 31.4 in 3. 62.8 in 4. 15.7 in 2. The circumfere

Augmented matrix, Consider the following system of linear equations. X 1...

Consider the following system of linear equations. X 1 +x 3 +x 4 = 2 X 1 +x 2 +x 3 = 6 X 2 +x 3 +x 4 = 3 X 1 +x 2 +x 4 = 0  (a) Write out the augmented matrix fo

Triangle inequalities, poa is a straight line in circle,wher o is center of...

poa is a straight line in circle,wher o is center of circle,b is any pointjoined with p.prove that pa>pb

#title.automotive cruise control system., What are some of the interestingm...

What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems

Between that two call numbers should she place the book, A librarian is ret...

A librarian is returning library books to the shelf. She uses the call numbers to denote while the books belong. She requires placing a book about perennials along with a call numb

Rate -categories of multiplication, Rate - when we know how many objects...

Rate - when we know how many objects are in a set, and need to find out the total number in several copies of that set. (e.g., if a child uses 4 copybooks in a year, how many co

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