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Math Help - Members in the Powerset.

  1. #1
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    Members in the Powerset.

    I have the following 3 sets.

    A = {1, 2, 3, 4, 5}, B = {a, b, c, d, e}, C = {red, green, blue}

    I want to compute the following |\wp(A*B*C)|

    So would I first find out how many values are in A*B*C

    Which I think is 5*5*3 = 75

    So to compute how many values are in the powerset, would I do 2^75? (Should be 2 to the power of 75.)

    This gives the result of 3.77789319 * 10^22

    Am I doing this correct?
    Last edited by richtea9; November 4th 2011 at 01:14 PM.
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  2. #2
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    Re: Members in the Powerset.

    Quote Originally Posted by richtea9 View Post
    I have the following 3 sets.
    A = {1, 2, 3, 4, 5}, B = {a, b, c, d, e}, C = {red, green, blue}
    I want to compute the following |\wp(A*B*C)|
    Your notation is a bit off (i.e. non-standard).
    I think that you want |\mathcal{P}(A\times B\times C)|=2^{|A|\cdot|B|\cdot|C|\cdot}.

    If that is not what you mean, please clear things up.
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  3. #3
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    Re: Members in the Powerset.

    Quote Originally Posted by Plato View Post
    Your notation is a bit off (i.e. non-standard).
    I think that you want |\mathcal{P}(A\times B\times C)|=2^{|A|\cdot|B|\cdot|C|\cdot}.

    If that is not what you mean, please clear things up.
    Yeah, I want the powerset of the cartesian product of a, b, c (A*B*C).

    Are we on the same lines?
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  4. #4
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    Re: Members in the Powerset.

    Quote Originally Posted by richtea9 View Post
    Yeah, I want the powerset of the cartesian product of a, b, c (A*B*C). Are we on the same lines?
    Exactly the same.
    So the answer is 2^{75}.
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  5. #5
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    Re: Members in the Powerset.

    Quote Originally Posted by Plato View Post
    Exactly the same.
    So the answer is 2^{75}.
    Perfect, thought so, thanks for the help.
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