Results 1 to 2 of 2

Math Help - can sum1 pls show me an example of this...

  1. #1
    Newbie
    Joined
    Aug 2006
    Posts
    12

    can sum1 pls show me an example of this...

    By considering each element of R,determine the relation R' on X with the smallest number of elements satisfying;
    (i)R proper subset R'
    (ii)R' is symmetric
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    (i)R proper subset R'
    I think you mean that R' is a proper subset of R, right?
    Cuz, otherwise you have this problem.
    ---
    Let X be a finite set. Then R can have at most n^2 elements where |X|=n. So you are saying that given any Relation R on X then you can find another relation R' on X that contains R which means that |R'|>|R|. But since R' is a relation on X there exists (according to your hypothesis) another set R'' that containts R' thus, |R''|>|R'|. But then you can use this argument again and again until your relation on X that has cardinality greater than n^2, which is impossible.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 18th 2011, 09:31 AM
  2. Using the MVT to show this
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 25th 2010, 11:19 AM
  3. Show that x =
    Posted in the Algebra Forum
    Replies: 8
    Last Post: November 25th 2010, 03:43 AM
  4. Show the sum
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 21st 2010, 03:28 AM
  5. how to show show this proof using MAX
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 14th 2009, 12:05 PM

Search Tags


/mathhelpforum @mathhelpforum