# Thread: Relations - Set Theory

1. ## Relations - 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 !!

2. contains R^n.
...How is this relation defined?

3. Originally Posted by WeeG
hello everyone,

R contains R^n.
I mean that R is included in R^n

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

4. If $R$ is a relation between sets $A$ and $B$: that is, $R \subseteq A \times B$, and similarly $S$ is a relation between $B$ and $C$, then the composition $R \circ S$ is the relation between $A$ and $C$ given by $\{ (a,c) \in A \times C : (a,b) \in R \mbox{ and } (b,c) \in S \mbox{ for some } b \in B \}$.

If $R$ is a relation between $A$ and itself, then it makes sense to define $R^2$ as $R \circ R$ and more generally $R^n = R \circ R^{n-1}$. Of course it turns out that composition is associative so that all the possible ways of defining $R^n$ are the same.

5. thanks a lot !!!!

I am impressed !!

thanks !

6. That's the rgep we know...

Alright Weeg, can you tackle it now?