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Homework Help: Show that B can't be a proper subset of A

  1. Jul 22, 2011 #1
    1. The problem statement, all variables and given/known data
    Let f be a function on A onto B where B is a subset of A, and f is a one-to-one function.
    Now, I want to show that B can't be a proper subset of A( that is, not B[itex]\subset[/itex]A. this means B=A).

    2. Relevant equations

    3. The attempt at a solution
    I attempted to solve this problem. Even though it is not complicated problem, but I don't have an idea how to prove it.

    Could you give me a clue or something??
  2. jcsd
  3. Jul 22, 2011 #2


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    Science Advisor
    Homework Helper

    hi gotjrgkr! :smile:

    if A is the integers and B is the even integers, and if f:A -> B is defined by f(n) = 2n,

    then f is onto and one-one, but B ≠ A :redface:
  4. Jul 22, 2011 #3
    Re: function

    Thank you!
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