hello everyone,

I have a problem with this question, I hope someone can help me out:

prove that a relations R over the set A is transitive if and only if for all n>=2 R contains R^n.

thanks !!

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- April 21st 2006, 12:52 PMWeeGRelations - Set Theory
hello everyone,

I have a problem with this question, I hope someone can help me out:

prove that a relations R over the set A is transitive if and only if for all n>=2 R contains R^n.

thanks !! - April 22nd 2006, 08:56 AMRebesquesQuote:

contains R^n.

- April 22nd 2006, 10:44 AMWeeGQuote:

Originally Posted by**WeeG**

I have no data except for that, it's a hard question....

:confused: - April 22nd 2006, 12:56 PMrgep
If is a relation between sets and : that is, , and similarly is a relation between and , then the composition is the relation between and given by .

If is a relation between and itself, then it makes sense to define as and more generally . Of course it turns out that composition is associative so that all the possible ways of defining are the same. - April 23rd 2006, 12:07 AMWeeG
thanks a lot !!!!

I am impressed !!

:)

thanks ! - April 23rd 2006, 08:19 PMRebesques
That's the rgep we know... :)

Alright Weeg, can you tackle it now?