Exercises of Relations and their property

**Kid** · Jun 1st 2010, 08:39 AM

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

Please help.

Thanks a lot

**Plato** · Jun 1st 2010, 08:56 AM

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

**Kid** · Jun 1st 2010, 09:10 AM

$R^2$ = {(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 ?

**Kid** · Jun 1st 2010, 09:29 AM

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:

**Plato** · Jun 1st 2010, 09:50 AM

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.

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

**Kid** · Jun 1st 2010, 10:00 AM

Originally Posted by Plato

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

Thank you so much for your ethusiastic and ability. I just learn by myself so sometimes I don't get it.

From now on if I have any problems I will post here to discuss with everyone. This is the first time I come here and I receive help immediately

That's cool.

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