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Math Help - Find a Set

  1. #1
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    Post Find a Set

    Im taking a mathematical proofs class and im thrown off on what the X's mean in this problem ! Any Advice?

    Let U={1,2,3,4} be the universal set, and let A={1,2,3}. Determine the set S={X e P(A) : lXl =the complement of lXl} by listing its elements
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  2. #2
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    Quote Originally Posted by nikie1o2 View Post
    Im taking a mathematical proofs class and im thrown off on what the X's mean in this problem ! Any Advice?

    Let U={1,2,3,4} be the universal set, and let A={1,2,3}. Determine the set S={X e P(A) : lXl =the complement of lXl} by listing its elements
    Sets contain elements. There is no rule that says these elements can't be sets themselves.

    The power set P(A), is defined as a set whose elements are all the possible subsets of set A. Hence, each and every element of P(A) is a set itself.

    When elements are not sets, we use lower case letters to denote them. When they are sets, then we use upper case letters to describe them.

    So X is just a set, which is a member of the set P(A). And hence the elements of X are elements of A. X is a subset of A.

    So you are being asked to find the set  S = \{X \in P(A) : |X| = |X^c|\}

    This translates, in english as:

    Find S, which is the set of all sets X, which are members of the power set of A, such that the cardinality of X is equal to the cardinality of the complement of X.
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