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Math Help - Surjective/Injective Proofs

  1. #1
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    Question Surjective/Injective Proofs

    I am having difficulties understanding how to build proofs and my instructor only puts some of them on the board, but never explains how he knows what to do to work proofs. I have an idea of how to build the proofs I am asking a question on, but am unsure how much information needs to be included. Please let me know how to build the following proof.

    Let f: A--->B and g: B--->A be functions where A & B are given sets. Prove that:

    a) f is injective if (g o f)(a)=a for all a elements in set A.
    b) f is surjective if (f o g)(b)=b for all b elements in set B.
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    Quote Originally Posted by s-sleedom2 View Post
    I am having difficulties understanding how to build proofs and my instructor only puts some of them on the board, but never explains how he knows what to do to work proofs. I have an idea of how to build the proofs I am asking a question on, but am unsure how much information needs to be included. Please let me know how to build the following proof.

    Let f: A--->B and g: B--->A be functions where A & B are given sets. Prove that:

    a) f is injective if (g o f)(a)=a for all a elements in set A.
    b) f is surjective if (f o g)(b)=b for all b elements in set B.
    I start you out on (a), to show f is injective we need to show if f(a) = f(b) then a=b for all a,b\in A.
    Say f(a) = f(b) \implies g(f(a)) = g(f(b)) \implies a = b.
    Thus, f is injective.
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