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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.

Discrete Math
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A 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.
Really? You think that way is easier to understand? How about just: A relation R on a set E is "anti-symmetric" if \[\forall x,y \in E(aRb \wedge bRa \Rightarrow a=b)\]
That'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

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Yeah, 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 2-tuples (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!

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