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One to one and onto

  1. Oct 13, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that f : X ! Y is 1-1 and onto if and only if for each set A [itex]\subset[/itex] X, f(A^c) = [f(A)]^c. ......c is a complement ....



    2. Relevant equations

    proof by contradiction.
    if f is not 1-1,there are x and y with f(x)=f(y)

    3. The attempt at a solution
    I was thinking if f is not onto ...then i can say A=X...BUT i can't figure it out..i can explain one to one or onto..i am just having hard time here.

    [
     
  2. jcsd
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