Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?