Results 1 to 8 of 8

Math Help - Equivalence Relations

  1. #1
    Member iPod's Avatar
    Joined
    Jul 2009
    Posts
    87

    Equivalence Relations

    I'm stuck with this equivelance relations question,

    'Let ~be the relation on the set Z of all integers defined by m~n provided that 10m+ n is divisible by 11.

    1. Prove that ~ is an equivalence relation.'

    First for reflexitivity, we do m~m and thus 10m+m=11m which surely is divisible by 11.

    Now for it being symmetric, we do n~m which means 10n+m and we need to prove that that is divisible by 11, however do not not how to prove this.

    Finaly for transitivity, I do not know how to approach it here - its kinda got me confused.

    Help would be very much appreciated, thank you very much.


    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,922
    Thanks
    1762
    Awards
    1

    fixed typo

    Quote Originally Posted by iPod View Post
    I'm stuck with this equivelance relations question,
    'Let ~be the relation on the set Z of all integers defined by m~n provided that 10m+ n is divisible by 11.
    1. Prove that ~ is an equivalence relation.'
    You see that m~n tells us that 10m+n=11k for some k.
    Can you see see that 10n+m=110k-99m?
    If so, is n~m?
    Last edited by Jhevon; November 8th 2010 at 08:28 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member iPod's Avatar
    Joined
    Jul 2009
    Posts
    87
    I'm sorry, but I wasn't able to get to your answer, all I have managed to do is;
    10n+m=(10m+n)+9n-9m
    10n+m=11k+9(n-m)

    could you hint me out how you got 10n+m=11(10k-9)??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,922
    Thanks
    1762
    Awards
    1
    10m+n=11k

    100m+10n=110k

    10n+m=110k-99m
    Follow Math Help Forum on Facebook and Google+

  5. #5
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by iPod View Post
    I'm stuck with this equivelance relations question,

    'Let ~be the relation on the set Z of all integers defined by m~n provided that 10m+ n is divisible by 11.

    1. Prove that ~ is an equivalence relation.'

    First for reflexitivity, we do m~m and thus 10m+m=11m which surely is divisible by 11.

    Now for it being symmetric, we do n~m which means 10n+m and we need to prove that that is divisible by 11, however do not not how to prove this.

    Finaly for transitivity, I do not know how to approach it here - its kinda got me confused.

    Help would be very much appreciated, thank you very much.


    Plato gave you the hint for symmetry. For transitivity, you want to show that if m~n and n~t, then m~t.

    m~n and n~t means that 10m + n = 11k and 10n + t = 11r for some integers k and r. In light of these two equations, what can we say about the expression 10m + t?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member iPod's Avatar
    Joined
    Jul 2009
    Posts
    87
    I have managed to get as far as 100m-t=11(k-r) but i cant get it in the form of 10m+t,

    is there a specific technique i could follow, because ive been trying for quite a long time and i concluded that there may be a technique that i am not aware of.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,922
    Thanks
    1762
    Awards
    1
    10m+n=11k\text{ and }10n+t=11j

    10m+11n+t=11k+11j

    So what in next?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member iPod's Avatar
    Joined
    Jul 2009
    Posts
    87
    I would like to point out that i just done the exact same method now and i got the answer lool :P
    10m+t=11(k+j-n)

    but this has actually helped expand my knowldge for answering questions in the future, thank you very much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equivalence relations
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: October 16th 2011, 03:53 PM
  2. Equivalence relations X x X
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: October 16th 2011, 11:53 AM
  3. Replies: 1
    Last Post: September 19th 2011, 02:09 PM
  4. Replies: 10
    Last Post: January 14th 2010, 01:28 PM
  5. equivalence relations
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 12th 2010, 08:17 PM

Search Tags


/mathhelpforum @mathhelpforum