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Thread: functions

  1. #1
    Super Member
    Feb 2008


    A,B,C are sets and f: A-->B and g: B-->C. Prove:

    1)If f and g are one-to-one, then so is g o f.
    2)If g o f is one-to-one, then g need not be one-to-one.

    Any advice?
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  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Dec 2007
    IISc, Bangalore
    Of course you know what to prove

    gof(x) = gof(y) $\displaystyle \rightarrow$ x = y

    Since g(f(x)) = g(f(y)) and g is one-one, we have f(x) = f(y). Since f is also 1-1, we have x=y.

    2) is nice, I will give you a general hint,try it

    General Hint: Draw a few blobs(actually 3, they are the sets). Mark some points in them(they are the elements). Now map points from one blob to another, remembering they conditions in data. Try your best to prove the question wrong. You will see why it must be right. Geometric intuition is your best pal, learn to use him.
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