Results 1 to 5 of 5

Math Help - Help with functions given 2 sets

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    39

    Help with functions given 2 sets

    I am working on a homework assignment for school. I am having problems with my homework. I have started to work out the question, but I seem to be getting stuck. I am not sure if what I have is correct or not. This is the question that I am currently working on.


    Question: Let A={1,2,3,4} and B={x,y,z}
    a) List the five functions from A to B.
    b) How many functions f: A -> B are there?
    c) How many functions f: A -> B are one-to-one?
    d) How many functions g: B -> A are there?


    Answers:
    a) I have only been able to come up with 3 functions. I thought of the functions as having ordered pairs so I came up with this as an answer.
    f(A) = {(1,x), (2,y). (3,z), (4,x)}
    f(A) = {(1,y), (2,z), (3,x), (4,y)}
    f(A) = {(1,z), (2,x), (3,y), (4,z)} from here I am not sure of what the last two functions would be. Also not sure if this is the correct way to solve this problem.


    b) I came up with the answer 3^4 to equal 81 functions
    c) I came up with there are no one-to-one functions
    d) I came up with 4^3 to equal 64 functions
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1

    Re: Help with functions given 2 sets

    Quote Originally Posted by needhelp101 View Post
    I am working on a homework assignment for school. I am having problems with my homework. I have started to work out the question, but I seem to be getting stuck. I am not sure if what I have is correct or not. This is the question that I am currently working on.


    Question: Let A={1,2,3,4} and B={x,y,z}
    a) List the five functions from A to B.
    b) How many functions f: A -> B are there?
    c) How many functions f: A -> B are one-to-one?
    d) How many functions g: B -> A are there?


    Answers:
    a) I have only been able to come up with 3 functions. I thought of the functions as having ordered pairs so I came up with this as an answer.
    f(A) = {(1,x), (2,y). (3,z), (4,x)}
    f(A) = {(1,y), (2,z), (3,x), (4,y)}
    f(A) = {(1,z), (2,x), (3,y), (4,z)} from here I am not sure of what the last two functions would be. Also not sure if this is the correct way to solve this problem.


    b) I came up with the answer 3^4 to equal 81 functions
    c) I came up with there are no one-to-one functions
    d) I came up with 4^3 to equal 64 functions
    They are correct.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    39

    Re: Help with functions given 2 sets

    My functions so far for part A are correct? If that is the case, I am unsure of how to find the last 2 functions. The question is asking for 5 functions, but I only have 3.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,790
    Thanks
    1687
    Awards
    1

    Re: Help with functions given 2 sets

    Quote Originally Posted by needhelp101 View Post
    My functions so far for part A are correct? If that is the case, I am unsure of how to find the last 2 functions. The question is asking for 5 functions, but I only have 3.
    How about: $\{(1,x),(2,x),(3,x),(4,x)\}~\&~\{(1,x),(2,x),(3,x ),(4,y)\}$
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2009
    Posts
    39

    Re: Help with functions given 2 sets

    Oh wow. That just makes me feel dumb. I'm not sure why I was thinking that I could not do that. Thanks. Also, my other answers look correct? And the way that I am saying that these are functions are correct? For example, the 3 functions that I came up with f(A) is correct? Or would I have to write it out as f: (A -> B) = {....}?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Functions Sets
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: April 23rd 2013, 11:08 AM
  2. Functions / Sets / Finite Sets
    Posted in the Discrete Math Forum
    Replies: 19
    Last Post: March 27th 2013, 10:33 PM
  3. Sets and functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 12th 2009, 11:14 AM
  4. Sets/Functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 1st 2007, 05:38 PM
  5. Sets and functions
    Posted in the Discrete Math Forum
    Replies: 12
    Last Post: August 21st 2007, 04:24 PM

Search Tags


/mathhelpforum @mathhelpforum