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    Question discrete mate

    4. Let
    A, B be finite sets. Recall that |A B| = |A| + |B| - |A B|. Find a similar formula
    for |A
    B C| using formal proof.


    thank q for who helping.......

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    Quote Originally Posted by cclia View Post
    4. Let
    A, B be finite sets. Recall that |A B| = |A| + |B| - |A B|. Find a similar formula
    for |A
    B C| using formal proof.


    thank q for who helping.......

    Hello,

    |A \cup B \cup C|=|D \cup C|

    So consider A \cup B=D

    Now use the formula you're given :

    |D \cup C|=|D|+|C|-|C \cap D|

    This gives =|A \cup B|+|C|-|(A \cup B) \cap C|

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

    =|A|+|B|+|C|-|A \cap B|-\left(|A \cap C|+|B \cap C|-|A \cap C \cap B \cap C| \right)

    =|A|+|B|+|C|-|A \cap B|-|A \cap C|-|B \cap C|+|A \cap B \cap C|
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