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Math Help - Another set theory

  1. #1
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    Exclamation Another set theory

    Let X be a finite set. Show that P(X) has 2^|x| elements. Also, show that |2^x|=2^|x|.

    {Hint: to give a rigorous proof, induct on the number of elements of X.}
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by r7iris View Post
    Let X be a finite set. Show that P(X) has 2^|x| elements. Also, show that |2^x|=2^|x|.

    {Hint: to give a rigorous proof, induct on the number of elements of X.}
    what does small x represent? and by P(X) you mean the power set of X correct?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    what does small x represent? and by P(X) you mean the power set of X correct?
    |x| is the number of member in set X.
    P(X) is the power set of X.
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  4. #4
    Senior Member tukeywilliams's Avatar
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    A subset  A \subseteq X is determined by deciding whether each of the  n elements of  X is in the subset: there are two possibilities for each element  x , namely  x \in A and  x \not \in A . So the total number of possibilities for the subset  A is  2 \times 2 \times \ldots \times 2 = 2^n . So  |\mathcal{P}(X)| = 2^{|x|} . Use this to be more rigorous.
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