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Math Help - Exercises of Relations and their property

  1. #1
    Kid
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    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

    Please help.

    Thanks a lot
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  2. #2
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    Please list what you get for \mathcal{R}^2.
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  3. #3
    Kid
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    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 ?
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  4. #4
    Kid
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    Quote Originally Posted by Plato View Post
    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:

    Last edited by Kid; June 1st 2010 at 09:55 AM.
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  5. #5
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    Quote Originally Posted by Kid View Post
    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)
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  6. #6
    Kid
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    Quote Originally Posted by Plato View Post
    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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