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Thread: Prove that the composite g o f: X->Z is also a bijection and that

  1. #1
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    Prove that the composite g o f: X->Z is also a bijection and that

    9.5 on picture. https://imgur.com/a/hwoI1oi
    Last edited by math951; Aug 28th 2019 at 07:25 PM.
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    Re: Prove that the composite g o f: X->Z is also a bijection and that

    just to be clear: to help solve this problem, we use a proposition used in the chapter. The proposition states that if we have a function f: X->Y and a function g:Y->X, they are inverses of each other if and only if g o f = Identity function of X, and f o g = Identity function of Y. I am aware how to prove this. I am not fond of the solution in the book for this problem. Or, I guess I do not understand the solution they use. here is there solution: https://imgur.com/a/SyOIWdn

    In the solution, why do they omit the Identity function of Y?
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    Re: Prove that the composite g o f: X->Z is also a bijection and that

    Found out how to solve this...from chapter 8 we had a propety that f o Identity function of x = f = identity function kf y o f.....
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    Re: Prove that the composite g o f: X->Z is also a bijection and that

    I was wrong...sigh...can anyone help me out here.
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