# Thread: Exercises of Relations and their property

1. ## Exercises of Relations and their property

Hello everybody,

Could you show me how to solve this kind of problem:

Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1,1), (1,2), (1,3), (2,3), (2,4), (3, 1), (3,4), (3, 5), (4, 2), (4, 5), (5, 1), (5, 2), and (5,4). Find:

a. $\displaystyle R^2$.
b. $\displaystyle R^3$.
c. $\displaystyle R^4$.
d. $\displaystyle R^5$.

The number of pairs in $\displaystyle R^n$ must small or equals to R or can be any without conditions ? Because I tried to do but the number of pairs in $\displaystyle R^2$ are larger than R

Thanks a lot

2. Please list what you get for $\displaystyle \mathcal{R}^2$.

3. $\displaystyle R^2$ = {(1,1),(1,2),(1,3),(1,4),(1,5),(2,1),(2,2),(2,4),( 2,5),(3,1),(3,2),(3,3),(3,4),(3,5),(4,1),(4,2),(4, 3),(4,4),(5,1),(5,2),(5,3),(5,4),(5,5)}

Is it correct ?

4. Originally Posted by Plato
This is why I asked you to list $\displaystyle \mathcal{R}^2$.
How do you get $\displaystyle (1,2)\in\mathcal{R}^2?$
I dunno, I just draw the map and connect all the numbers that exists on R. Then I find which way can go from R to R. That's $\displaystyle R^2$, I think.

For example:

5. Originally Posted by Kid
I dunno, I just draw the map and connect all the numbers that exists on R. Then I find which way can go from R to R. That's $\displaystyle R^2$, I think.
I think that you have it correct. It contains all pairs but $\displaystyle (2,3)~\&~(4,5)$
I think that you have it correct. It contains all pairs but $\displaystyle (2,3)~\&~(4,5)$