1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Set Theory? question

  1. Mar 13, 2016 #1
    1. The problem statement, all variables and given/known data

    f: X ----> Y and g: Y ----> Z

    be functions and let

    h = g o f: X ----> Z

    2. Relevant equations

    a. If h is surjective then g is surjective

    b. If h is surjective then f is surjective.

    3. The attempt at a solution


    h: X ----> Z

    Suppose h: x ---> z is surjective for ∈ Z. Since h is surjective ∃a ∈ X such that
    h(a) = g(f(a)) = k

    Now let y = f(a) ∈ Y so...
    g(y) = g(f(a)) = k; as declared QED.

    Suppose h: x ---> z is surjective for y.........I'm not even sure how to start.

    PS: To be honest, I really need to find a good textbook on proofs because my lecturer is outright atrocious. If anyone knows of any texts, do post me some recommendations as well.
  2. jcsd
  3. Mar 13, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your proof of a) looks quite good. You didn't say what k is, but it's fairly obvious.

    Why do you think b) is true?
  4. Mar 13, 2016 #3
    k is just an integer that belongs to set Z.

    As for b, I think f is surjective because h is. Since f is an input of g, I'm not exactly sure how I can re-utilise my proof from part a.
  5. Mar 13, 2016 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If I can't see how to prove something, I usually try to disprove it and see what happens.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Theory question Date
Simple set theory question Sep 11, 2017
Set theory question Sep 7, 2017
Some true or false Field extension theory questions Dec 4, 2016
Galois Theory questions Dec 4, 2016
Set Theory Question Oct 11, 2016