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Injectivity vs. surjectivity

  1. Feb 2, 2009 #1
    Let f: A->B and g: B->C
    a. C0[tex]\subset[/tex]C, show that (g o f)-1(C0))=f-1(g-1(C0)).
    b. If f and g are injective, show that g o f is injective
    c. If g o f is injective, what can you say abuot injectivity of f and g?
    d. If f and g are surjective, show that g o f is surjective.
    e. If g o f is surjective, what can you say about surjectivity of f and g.
    f. Summarize your answers to (b)-(e) in the form of a theorem

    I don't know how to do this.... can someone else me..?

    Thank You
  2. jcsd
  3. Feb 2, 2009 #2


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    Science Advisor
    Homework Helper

    Hi tomboi03! :wink:

    Show us what you've tried, and where you're stuck, and then we'll know how to help.

    Start with part a. … take a typical member of the LHS, and prove that it is in the RHS … then do it the other way round. :smile:
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