Results 1 to 3 of 3

Math Help - Quick explanation

  1. #1
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303

    Quick explanation

    Suppose the set A has m elements and the set B has n elements. There are 2^(m*n) relations from A to B and n^m functions from A to B.

    Can some one just give me combinatorial explanation. I don't really need to see anything worked out.

    Thanks,
    --Dan
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by Danneedshelp View Post
    Suppose the set A has m elements and the set B has n elements. There are 2^(m*n) relations from A to B and n^m functions from A to B.
    You need to recall that any relation from A to B is a subset of A \times B.
    If \left| A \right| = m~\& ~\left| B \right| = n \Rightarrow \quad \left| {A \times B} \right| = m \cdot n\quad .
    There are 2^{\left| {A \times B} \right|}  = 2^{mn} subsets of A \times B.

    There it is!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517

    Second Part

    The second part is because there are n choices to send the first element in A to, n choices to send the second element in A to, n choices to send the ...., n choices to send the mth element to. That is n^m distinct choices.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Quick absolute value inequality explanation, please
    Posted in the Pre-Calculus Forum
    Replies: 10
    Last Post: February 10th 2011, 10:00 AM
  2. Quick explanation of integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2009, 12:56 PM
  3. Replies: 6
    Last Post: March 5th 2009, 04:34 AM
  4. Replies: 3
    Last Post: April 11th 2008, 06:46 PM
  5. need an explanation
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 4th 2006, 01:35 PM

Search Tags


/mathhelpforum @mathhelpforum