Results 1 to 4 of 4

Math Help - Sets/Functions

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    4

    Sets/Functions

    Hi! I have a question regarding Sets and Functions, please help, thanks!

    I have set A{1,2,3,4,5}, B{3,4,5,6,7}, C{5,6,7,8,9}

    A union B = {1,2,3,4,,6,7}
    A intersection B = {3,4,5}

    Define an onto(surjective) function f: A union B -> A intersection B
    Define an 1-1 function f: A union B -> A intersection B

    2nd part--
    Let U = A union B union C
    Let D = {x|x,y,z in U) ^ (there exits y)(there exists z)(z = x * y)

    U = {1,2,3,4,5,6,7,8,9}
    I am not sure how to get set D.
    Do I choose a value for y and z from set U and if there is an value for x inside Set U satstify the equation? and if it does, the value for x goes in set D?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,901
    Thanks
    329
    Awards
    1
    Quote Originally Posted by darken4life View Post
    2nd part--
    Let U = A union B union C
    Let D = {x|x,y,z in U) ^ (there exits y)(there exists z)(z = x * y)

    U = {1,2,3,4,5,6,7,8,9}
    I am not sure how to get set D.
    Do I choose a value for y and z from set U and if there is an value for x inside Set U satstify the equation? and if it does, the value for x goes in set D?
    Basically. I'd choose an x, say x = 1. Then try to find a y such that z = x \cdot y such that z \in U.

    For example: y = 1. Thus we ask the question is z = 1 \cdot 1 \in U? Yes. So 1 \in D.

    etc for all values of y that create an appropriate z.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2007
    Posts
    4
    Thanks! I got it clearly.
    Can you help me on the first part?
    Is not that I want you guys to answer it for me but simply the question.

    Define an onto(surjective) function f: A union B -> A intersection B
    -if A is union B then A is intersection B
    How I define an function out of that?
    Not sure on how to approach this.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,901
    Thanks
    329
    Awards
    1
    Quote Originally Posted by darken4life View Post
    Thanks! I got it clearly.
    Can you help me on the first part?
    Is not that I want you guys to answer it for me but simply the question.

    Define an onto(surjective) function f: A union B -> A intersection B
    -if A is union B then A is intersection B
    How I define an function out of that?
    Not sure on how to approach this.
    The surjective function is easy: Just make up any function you like. For example, consider:
    f: \{1, 2, 3, 4, 5, 6, 7 \} \to \{3, 4, 5 \}:
    f(1) = 3
    f(2) = 3
    f(3) = 4
    f(4) = 4
    f(5) = 5
    f(6) = 5
    f(7) = 4

    For each element in the codomain there is at least one element that exists in the domain.

    The one to one function is rather harder: in fact it is impossible. In order to have a one to one function between sets they must have the same cardinality. These sets don't.

    Though if we are allowed to restrict the domain to three elements, for example, we can do it:
    f: \{2, 3, 4 \} \to \{3, 4, 5 \}:
    f(2) = 4
    f(3) = 5
    f(3) = 3
    is one example.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sets and functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 2nd 2010, 09:51 PM
  2. functions between sets
    Posted in the Discrete Math Forum
    Replies: 14
    Last Post: January 26th 2009, 08:28 PM
  3. a little bit of functions on sets
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: October 15th 2008, 06:06 PM
  4. More sets and functions
    Posted in the Discrete Math Forum
    Replies: 14
    Last Post: August 24th 2007, 11:08 AM
  5. Sets and functions
    Posted in the Discrete Math Forum
    Replies: 12
    Last Post: August 21st 2007, 04:24 PM

Search Tags


/mathhelpforum @mathhelpforum