Register

Quasi- Order Relations

912 views
0 votes
0 votes

What are the conditions for a relation to be quasi-ordered?

In NPTEL video lectures, I found conditions for it to be Irreflexive and Transitive.
But on Wikipedia and other resources, it's given that a binary relation R on a set A quasi-order if it is Reflexive and Transitive.

Which one is correct ? or Am I missing something?

User Avatar

1 Answer

2 votes
2 votes

MIT : A relation R  is called a quasi-order relation if it is reflexive and transitive,
https://www.sciencedirect.com/science/article/pii/S0012365X97000897

NPTEL : Let R be a binary relation on a set A, R is a quasi order if R is transitive and irreflexive.

Stack Exchange : A relation R  is called a quasi-order relation if it is reflexive and transitive,

https://math.stackexchange.com/questions/2186697/example-of-quasi-order-on-a-set

ODU University : A binary relation R on a set A is a quasi order if and only if it is  irreflexive, and  transitive. 
A quasi order is necessarily antisymmetric as one can easily verify. http://www.cs.odu.edu/~cs381/cs381content/relation/order/order.html

I guess there is No universally accepted definition. If something concrete comes up..Let me know too. 

And til then, Don't worry..Won't come in GATE or they will define it.

User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
1 answer
1
Sona Barman asked Mar 8, 2019
684 views
General Topic Doubt Set Theory & Algebra: Relations
How to check a relation is transitive or not from its matrix representation? Please help me with an example.
How to check a relation is transitive or not from its matrix representation? Please help me with an example.
User Avatar
0 votes
0 votes
1 answer
2
srestha asked Mar 7, 2019
862 views
Ace Test Series: Set Theory & Algebra - Relations
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________ Ans given 48 but I got 8 Please verify
Let $A=\left \{ 1,2,3 \right \}$. Number of relation on $A$ which are neither reflexive, nor irreflexive but symmetric is ___________Ans given 48but I got 8Please verify
User Avatar
0 votes
0 votes
1 answer
3
Abhipsa asked Jan 23, 2019
552 views
Functions and Relations
What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ? Thanks.
What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ? Thanks.
User Avatar
0 votes
0 votes
1 answer
4
Abhipsa asked Jan 23, 2019
417 views
Relations
Consider the following relation: $R={(x,y)| y=x^i, ∃ “i” in Z }$ R is i) Reflexive ii) Symmetric iii) Anti symmetric iv) Transitive Thanks!
Consider the following relation:$R={(x,y)| y=x^i, ∃ “i” in Z }$R isi) Reflexiveii) Symmetriciii) Anti symmetriciv) TransitiveThanks!
User Avatar
Link Copied!