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Math Help - Set Proof

  1. #1
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    Set Proof

    THM: (A-B) - C = (A-C) - (B -C)\ \ \forall sets A,B,C.

    Prove the above thm.
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  2. #2
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    \begin{array}{l}<br />
 \left( {A \cap C^c } \right) \cap \left( {B \cap C^c } \right)^c  \\ <br />
 \left( {A \cap C^c } \right) \cap \left( {B^c  \cup C} \right) \\ <br />
 \left( {A \cap C^c  \cap B^c } \right) \\ <br />
 \end{array}<br />
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  3. #3
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    Quote Originally Posted by Plato View Post
    \begin{array}{l}<br />
 \left( {A \cap C^c } \right) \cap \left( {B \cap C^c } \right)^c  \\ <br />
 \left( {A \cap C^c } \right) \cap \left( {B^c  \cup C} \right) \\ <br />
 \left( {A \cap C^c  \cap B^c } \right) \\ <br />
 \end{array}<br />
    I appreciate it. I believe the C^c for instance means the compliment of C (that is everything that is not C)- is there another way to prove this? I don't quite see how it proves it. Thanks for the explanation.
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  4. #4
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    \left( {A \cap C^c  \cap B^c } \right) = \left( {A \cap B^c } \right) \cap C^c  = \left( {A\backslash B} \right)\backslash C<br />
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