Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Sets and functions

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data

    f: A -> B is a function with C a subset of B. Prove that
    f(f^-1(C)) = [C intersection Im(f)]. (f^-1(c) = f inverse of C)

    2. Relevant equations



    3. The attempt at a solution

    Please let me know how to approach to the solution (not using venn diagrams). Also if possible give me any link that gives tips on approaching any general sets and functions problem.
    Thank you.
     
    Last edited: Sep 1, 2010
  2. jcsd
  3. Sep 1, 2010 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    What's K?
     
  4. Sep 1, 2010 #3

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    By K did you mean C?

    Usually when you want to prove two sets are equal to each other, you prove each is a subset for the other. If [tex]y\in f(f^{-1}(C))[/tex] can you prove that [tex] y\in C\cap Im(f)[/tex]? Then you would have that [tex]f(f^{-1}(C))\subset C\cap Im(f)[/tex]. Do the other way also and you're done
     
  5. Sep 1, 2010 #4
    I am sorry, that C.. how can I prove that y belongs to c intersection im(f)?
     
  6. Sep 1, 2010 #5

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, you have some property that y satisfies because we know it belongs to [tex]f(f^{-1}(C))[/tex], which you should try to write down. Then use it
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook