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A question in set theory

  1. Mar 7, 2006 #1
    i need to prove that next three arguments are equivalent:
    1)f:X->Y is on Y.
    2) f:p(X)->p(Y) is on p(Y).
    3)f^-1:p(Y)->p(X) is one-to-one correspondence.
    where p is the power set.
     
  2. jcsd
  3. Mar 7, 2006 #2

    matt grime

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    what does 'on' mean? onto? perhaps playing devils advocate a little, but mainly to make you think about the question, if f is defined on X, how is it then defined on its power set (usually denoted P(X), not p(X)).
     
  4. Mar 8, 2006 #3
    yes, i checked in mathworld, it's onto.
    my main problem is with the third statement, i tried imply 3 from 1 and vice versa, but i don't know how to formualte the proof.

    any further hints are appreciated.
     
  5. Mar 8, 2006 #4
    are we assuming the function is unary?
    or rather f(s in p(Y)) can be distributed into each element of s since
    s is a subset of elements in Y?
     
  6. Mar 9, 2006 #5
    no, we don't assume it's unary.
    about your second question do you mean if B is a subset of P(Y) then
    f:B->f(B)={f(x)|x belongs to B} then yes, otherwise no.
     
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