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Question about sets.

  1. Nov 15, 2006 #1
    how do i show that Y^(XU{x})=(Y^X)x(Y^{x}) where X and Y are finite sets, and {x} is a singleton.
    obvisouly i need to show that one set is contained in another and vice versa, the problem is how to do so?
     
    Last edited: Nov 15, 2006
  2. jcsd
  3. Nov 18, 2006 #2
    for those who havent undersatand, i need to prove |Y^X|=|Y|^|X|
    i tried to prove it in induction on the exponent but i got to what i posted in the first post in this thread, can someone help me on this here?
     
  4. Nov 18, 2006 #3

    matt grime

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    Just write down a bijection, in the first post. Though the result you want to prove in the second post follows from counting the elements directly.
     
  5. Nov 18, 2006 #4
    you mean because the set of all functions from X to Y, its cardinal equals the number of possible mappings from X to Y, which is |Y|^|X|, right?
    still i think that i need a rigorous proof for this, and counting isnt as rigouros.
     
  6. Nov 18, 2006 #5

    matt grime

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    Of course counting is rigorous.
     
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