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Some basic definition questions of set theory

  1. Apr 20, 2004 #1
    I have to prove the following theorem,

    1) If f:A->B is a surjection, and g:B->C is a surjection then g dot f:a->C is a surjection

    Well this makes sense and I am not sure how to PROVE it

    Is it sufficient to say the following

    if for every element b of B, there exists a element a of A such that f(a)=b and same for B->C for g(b)=c is true, Then

    for every element of c in C, there must exist an a of A such that g(f(a))=c since for every b in B there exists f(a)=b, and we know g(b)= c is true for every element of c,
    Last edited: Apr 20, 2004
  2. jcsd
  3. Apr 21, 2004 #2

    matt grime

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    Yes that's the right idea though the phrase 'we know g(b)=c is true for every..' is, erm, not what you want to write, but I think that is just the sentence structure nothing more.

    You must show that for all c in C, there is an a in A such that gf(a)=c, which is what you've done.
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