Results 1 to 4 of 4

Math Help - types of functions

  1. #1
    Junior Member
    Joined
    Jul 2006
    Posts
    73

    types of functions

    (a) Suppose that the set A has exactly two elements and the set B has exactly three. You have to construct explicitly all functions from A to B, and to decide whether each of them is injective and surjective. There are nine such functions let us label them (arbitrarily) as f1, f2, . . ., f9.
    Let A = {1, 2}, and B = {a, b, c}. In the table below fill out all possible values of f1,
    f2, . . ., f9 on 1 and 2.

    Function fi(1) fi(2) Injective? Surjective?
    f1 a a No No
    f2 a b Yes No
    f3 a c Yes No
    f4 ? ? ? ?
    f5 ? ? ? ?
    f6 ? ? ? ?
    f7 ? ? ? ?
    f8 ? ? ? ?
    f9 ? ? ? ?

    (b) Now let A has exactly three elements and B has exactly two: A = {1, 2, 3}, B = {a, b}.
    Again, construct explicitly all functions from A to B and determine whether they are injective and surjective. Put your results in a table similar to the table in part (a).
    (c) Let the set A have exactly m elements and B have exactly n (where n,m 2 N). How many different functions are there from A to B?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    If |A|<|B| there are NO surjections from A to B and permut(|B|,|A|) injections.

    The number of mapping from A to B is \left| B \right|^{\left| A \right|}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2006
    Posts
    73
    Right, I know all the rules, I have this in my notes....I am still having problems with this problem because there are no other similiar examples in my book..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Plato View Post
    If |A|<|B| there are NO surjections from A to B and permut(|B|,|A|) injections.

    The number of mapping from A to B is \left| B \right|^{\left| A \right|}.
    What happens if |B|=3 and |A|=\aleph_0. Then what is 3^{\aleph_0}?

    Note, It is understandable to me when |B|=2 then 2^{\aleph_0}=|\mathcal{P}(A)|
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: March 25th 2011, 04:26 AM
  2. Types of variables
    Posted in the Statistics Forum
    Replies: 2
    Last Post: August 2nd 2010, 07:37 PM
  3. Types of Derivatives.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 21st 2010, 06:09 AM
  4. Types of Conics.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: July 7th 2008, 09:03 PM
  5. types of functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 18th 2007, 11:06 PM

Search Tags


/mathhelpforum @mathhelpforum