Sorry, but I'm in dire need(Proofs)

  1. Hello, I need some help. Could someone kick me(hard please) in the right direction here? Here are the statements I need to prove:
    1) If g of f is injective, then f is injective
    2) If g of f is subjective, then g is subjective

    where g and f are functions where f:A->B and g:B -> C where A,B and C are sets

    Any kicks in the right direction would be GREATLY appreciated. Thank you.
     
  2. jcsd
  3. Both can be done easily by contradiction.
     
  4. Curious3141

    Curious3141 2,970
    Homework Helper

    Start with the definitions of injections and surjections (note the spelling of the latter), and draw functional mappings (domain/codomain diagrams). The proof is fairly easy from inspecting the mappings.

    Wikipedia has fairly good pages on these subjects, complete with the mappings you need for the proof : http://en.wikipedia.org/wiki/Injective_function

    http://en.wikipedia.org/wiki/Surjection
     
    Last edited: May 16, 2006
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