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Math Help - Converting Sets to Set Builder Notation

  1. #1
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    Converting Sets to Set Builder Notation

    I have a problem I need to do, and I was wondering what the method is to convert set notation to set builder notation. The problem is:

    Show that if A, B, and C are sets than

    A \cup B \cup C = A + B + C - (A \cap B) - (A \cap C) - (B \cap C) + (A \cap B \cap C)

    If there is a better method than converting to set builder notation, let me know what it is (Although I would still like to know a general method from converting from this notation to a set builder notation).

    Thanks,
    James
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  2. #2
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    Quote Originally Posted by menmonmay View Post
    I have a problem I need to do, and I was wondering what the method is to convert set notation to set builder notation. The problem is:
    Show that if A, B, and C are sets than
    A \cup B \cup C = A + B + C - (A \cap B) - (A \cap C) - (B \cap C) + (A \cap B \cap C)

    If there is a better method than converting to set builder notation, let me know what it is
    It appears as if you are dealing with the number of elements in a set.
    That is denoted by |A| or perhaps \#(A).
    Thus your formula would be: |A\cup B\cup C|=|A|+|B|+|C|-|A\cap B|-|A\cap C| -|B\cap C|+|A\cap B\cap C|


    BTW: The LaTex for that is [tex]|A\cup B\cup C|=|A|+|B|+|C|-|A\cap B|-|A\cap C| -|B\cap C|+|A\cap B\cap C| [/tex].
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