# Exercises of Relations and their property

• June 1st 2010, 08:39 AM
Kid
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. $R^2$.
b. $R^3$.
c. $R^4$.
d. $R^5$.

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

Thanks a lot
• June 1st 2010, 08:56 AM
Plato
Please list what you get for $\mathcal{R}^2$.
• June 1st 2010, 09:10 AM
Kid
$R^2$ = {(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 ?
• June 1st 2010, 09:29 AM
Kid
Quote:

Originally Posted by Plato
This is why I asked you to list $\mathcal{R}^2$.
How do you get $(1,2)\in\mathcal{R}^2?$

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 $R^2$, I think.

For example:

http://i209.photobucket.com/albums/b...d91/dmath2.png
• June 1st 2010, 09:50 AM
Plato
Quote:

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 $R^2$, I think.

I think that you have it correct. It contains all pairs but $(2,3)~\&~(4,5)$
I think that you have it correct. It contains all pairs but $(2,3)~\&~(4,5)$