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Math Help - P(A)..Power set of A.

  1. #1
    Member
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    P(A)..Power set of A.

    Hey all,

    Given A = \{\emptyset, 1, \{2,3\}\}
    Is
    P(A) = \{\emptyset, 1, \{1,\{2,3\}\},\{2,3\}\} ?

    And also how can I prove that for all sets X and Y we have P(X) \cup P(Y) \subset P(X \cup Y)
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  2. #2
    Senior Member Tinyboss's Avatar
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    What is the cardinality of A (denoted |A|)? The cardinality of P(A) is 2^|A|, so what you wrote is missing a few. Also, the elements of P(A) are subsets of A, so there's no way that 1 is an element of P(anything), since it's not a set.

    I think once you get the first part straightened out, the second part won't give you much trouble.
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