Determine if r is equivalence relation or a partial ordering, Mathematics

Assignment Help:

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 partial ordering. 

Ans: R is described on the set P of cross product of set of positive integers Z+ as (a, b) R (c, d) iff a*d =b*c. Here now let us test if R is an equivalence relation or not  

Reflexivity: Let (x, x) be any element of P, after that since a*a = a*a , we can say the (a, a) R (a, a).So R is reflexive.  

Symmetry: Let (a, b) and (c, d) are any two elements in P like that (a, b) R (c, d). After that we have a*d = b*c => c*b = d*a => (c, d) R (a, b) => R is symmetric.   

Transitivity: Let assume (a, b), (c, d) and (e, f) are any three pairs in P like that (a, b) R (c, d) and (c, d) R (e, f). After that we have a*d = b*c  and c*f = d*e  => a/e = b/f => a*f = b*e => (a, b) R (e, f) => R is transitive.

Hence R is an equivalence relation.


Related Discussions:- Determine if r is equivalence relation or a partial ordering

Domain and range of a relation, Consider R be a relation from A to B, that ...

Consider R be a relation from A to B, that is, take R A Χ B. Then Domain R = {a: a € A, (a, b) € R for any b € B} i.e. domain of R is the set of all the first components of

Assignment help, How do get help with my work? should i just type it in thi...

How do get help with my work? should i just type it in this box...? sorry thanks!

Discrete, For each of these arguments determine whether the argument is cor...

For each of these arguments determine whether the argument is correct or incorrect and explain why. a) Everyone enrolled in the university has lived in a dormitory. Mia has never l

Find the least and greatest number of coins, Marc goes to the store with ex...

Marc goes to the store with exactly $1 in change. He has at least one of each coin less than a half-dollar coin, but he does not have a half-dollar coin. a. What is the least nu

Derivatives, What are the ingredients of a Mathematical Model? What is a mo...

What are the ingredients of a Mathematical Model? What is a model?

Prove that the height of the cloud , HE IGHTS AND DISTANCES If the ...

HE IGHTS AND DISTANCES If the angle of elevation of cloud from a point 'h' meters above a lake is α and the angle of depression of its reflection in the lake is  β , prove

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