A community for students.
Here's the question you clicked on:
 0 viewing
lljenjenll
 one year ago
is the relation antisymmetric?
A= {1,2,3,4,5}
R={(1,3),(1,1),(2,4),(3,2),(5,4),(4,2)}
the answer is no since (2,4) and (4,2) are in R. But I do not understand how.
lljenjenll
 one year ago
is the relation antisymmetric? A= {1,2,3,4,5} R={(1,3),(1,1),(2,4),(3,2),(5,4),(4,2)} the answer is no since (2,4) and (4,2) are in R. But I do not understand how.

This Question is Open

mp19uy
 one year ago
Best ResponseYou've already chosen the best response.1A relation has the antisymmetric property when, \[(a,b) \in R \Rightarrow (b,a) \notin R, \forall a,b \in A, a \neq b\] There is another definition, but I think this one is easier to understand. Another thing to remember is that, you can only have (a,b) and (b,a) in the relation if a=b.

Splash_Dance
 one year ago
Best ResponseYou've already chosen the best response.0Really? You think that way is easier to understand? How about just: A relation R on a set E is "antisymmetric" if \[\forall x,y \in E(aRb \wedge bRa \Rightarrow a=b)\]

mp19uy
 one year ago
Best ResponseYou've already chosen the best response.1That's the other definition that I was talking about, and it's equivalent to what I wrote: ', you can only have (a,b) and (b,a) in the relation if a=b.' Both are correct of course, and that one is the more commonly used, but I finally understand the difference between symmetric, antisymmetric and asymmetric after I wrote the property the way I did in my previous message. Of course that, if you are able to understand one, you should understand the other one. Bottom line, everyone understand math in a different way, it's cool to have more than one way to refer to the same property :D

Splash_Dance
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I totally agree. In fact, it's probably more useful to think of the property your way when thinking about a relation as a set of 2tuples (as the question was presented). Personally, I think the other way is more helpful when visualizing an ordering like so: dw:1383411428262:dw Anyway, great to hear your feedback!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.