Results 1 to 11 of 11

Math Help - functions and combinations

  1. #1
    Junior Member
    Joined
    Mar 2012
    From
    Turkey
    Posts
    26

    functions and combinations

    Let A = {a, b, c, d} and B = {e, f}. How many functions are there from A to B? How many are one-to-one? How many are onto?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Mar 2012
    From
    Turkey
    Posts
    26

    Re: functions and combinations

    There are 2^4 functions. Number of onto functions:C(4,2).2!
    I want to learn the number of one to one functions and how to find it step by step if it is possible?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,705
    Thanks
    1637
    Awards
    1

    Re: functions and combinations

    Quote Originally Posted by serhanbener View Post
    There are 2^4 functions. Number of onto functions:C(4,2).2!
    I want to learn the number of one to one functions and how to find it step by step if it is possible?
    There are 2^4-2 onto functions.
    There are no one-to-one functions.
    If |A|>|B| there are no one-to-one functions, A\to B.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2012
    From
    Turkey
    Posts
    26

    Re: functions and combinations

    If A and B had changed places how many one to one functions should have been?(I am sorry I didn't pay attention when asking the question)

    C(4,2).2!?
    How did you find the onto functions? What is the logic of the solution?
    Last edited by serhanbener; March 27th 2012 at 09:58 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2012
    From
    Turkey
    Posts
    26

    Re: functions and combinations

    Many Thanks for your help. There are 16 functions from A to B and there re only 2 that are not onto..
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,705
    Thanks
    1637
    Awards
    1

    Re: functions and combinations

    Quote Originally Posted by serhanbener View Post
    If A and B had changed places how many one to one functions should have been?(I am sorry I didn't pay attention when asking the question) How did you find the onto functions? What is the logic of the solution?
    If N=|A|\ge |B|=K then the number of onto functions A\to B is
    \sum\limits_{j = 0}^K {{{\left( { - 1} \right)}^j}\binom{K}{j}{{\left( {K - j} \right)}^N}}.

    See this page.
    Last edited by Plato; March 28th 2012 at 01:37 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Mar 2012
    From
    Turkey
    Posts
    26

    Re: functions and combinations

    S(A)=5 and S(B)=3. How many onto functions are there from set A to
    set B?
    I am trying to match 5 elements in set A with 3 elements in B. I can
    do that in 2 ways.
    3,1,1 or 2,2,1
    I chose 3 elements from set A C(5,2) and 1 element in C(2,1) ways.
    C(5,2)C(2,1).3!/2!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,705
    Thanks
    1637
    Awards
    1

    Re: functions and combinations

    Quote Originally Posted by serhanbener View Post
    S(A)=5 and S(B)=3. How many onto functions are there from set A to set B?
    Use the inclusion/exclusion summation I posted.
    \text{Surj}(5,3)=150. So the are 150 surjections from a set of five to a set of three.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Mar 2012
    From
    Turkey
    Posts
    26

    Re: functions and combinations

    Let's solve in my way:
    There are 2 choices: 311 and 221.C(5,3).C(2,1).3!/2!+C(5,2).C(3,1)C(2,1)3!/2!=150
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,705
    Thanks
    1637
    Awards
    1

    Re: functions and combinations

    Quote Originally Posted by serhanbener View Post
    Let's solve in my way:
    There are 2 choices: 311 and 221.C(5,3).C(2,1).3!/2!+C(5,2).C(3,1)C(2,1)3!/2!=150
    Could you show us this method for \text{Surj}(10,5) onto from a set of ten to a set of five?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    Mar 2012
    From
    Turkey
    Posts
    26

    Re: functions and combinations

    My way takes too much time in the question you have asked but my way is better than memorizing a formula. If there are 10 elements in the image set Binomial formula is better.
    Last edited by serhanbener; March 29th 2012 at 10:44 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinations of Functions
    Posted in the Algebra Forum
    Replies: 0
    Last Post: January 16th 2012, 02:41 PM
  2. Combinations of Functions
    Posted in the Algebra Forum
    Replies: 18
    Last Post: October 1st 2011, 02:06 PM
  3. Combinations of functions
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: July 16th 2010, 08:04 PM
  4. Combinations of Functions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 2nd 2009, 09:45 AM
  5. Combinations Of Functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 15th 2008, 04:50 PM

Search Tags


/mathhelpforum @mathhelpforum