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Math Help - Sets

  1. #1
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    Unhappy Sets

    Is there any direct formula to find the complement of (A-B)?
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  2. #2
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    Quote Originally Posted by matsci0000 View Post
    Is there any direct formula to find the complement of (A-B)?
    (complement of A) union (A intersect B)
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  3. #3
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    Complement of (A - B)

    Hello matsci0000
    Quote Originally Posted by matsci0000 View Post
    Is there any direct formula to find the complement of (A-B)?
    A slightly simpler version of the formula that HallsofIvy has given you is A' \cup B, where A' is the complement of A (which is sometimes written A^c).

    If you know the Laws of Sets, you can prove this as follows:

    First, the definition: A - B = A \cap B' (the elements that are in A but not in B)

    So (A-B)' = (A \cap B')'

    = A' \cup (B')' (De Morgan's Law)

    = A' \cup B (Involution Law)

    Grandad
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  4. #4
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    Thanks, Grandad, I didn't take the time to simplify.
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