Results 1 to 2 of 2

Math Help - Need help with a proof dealing with functions

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    79

    Question Need help with a proof dealing with functions

    Let f:A--->B be a function. Prove that f is surjective if and only if f^(-1)(W) does not equal the empty set for all nonempty sets W of B.

    I really do not know what to do with this. Thanks for your help everyone
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,661
    Thanks
    1616
    Awards
    1
    Quote Originally Posted by steph3824 View Post
    Let f:A--->B be a function. Prove that f is surjective if and only if f^(-1)(W) does not equal the empty set for all nonempty sets W of B.
    Because f is sujective \left( {\forall b \in B} \right)\left( {\exists a \in A} \right)\left[ {f(a) = b} \right]. Is it possible for f^{-1}(\{b\}) to be empty?

    Likewise if \left( {\forall b \in B} \right)\left[ {f^{ - 1} (\{ b\} ) \ne \emptyset } \right] must f be surjective?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Word problem: Dealing with functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 19th 2011, 04:38 PM
  2. Replies: 8
    Last Post: November 13th 2010, 07:14 PM
  3. proof dealing with lcm
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 16th 2009, 06:54 AM
  4. Help with a proof dealing with isometries
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 27th 2008, 07:24 PM
  5. Dealing with user-defined functions
    Posted in the Calculators Forum
    Replies: 0
    Last Post: October 27th 2008, 01:25 PM

Search Tags


/mathhelpforum @mathhelpforum