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Math Help - Proof involving sets

  1. #1
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    Exclamation Proof involving sets

    X \ ( A ^ B ) = ( X \ A ) U ( X \ B )

    I know I have to show (prove) containment in both directions to prove equality...but I'm not sure even where to start with this.

    Thanx in advance for the help!
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  2. #2
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    It is easy.
    \begin{array}{rcl}<br />
   {X\backslash \left( {A \cap B} \right)} &  \Leftrightarrow  & {X \cap \left( {A \cap B} \right)^c }  \\<br />
   {} &  \Leftrightarrow  & {X \cap \left( {A^c  \cup B^c } \right)}  \\<br />
   {} &  \Leftrightarrow  & {\left( {X \cap A^c } \right) \cup \left( {X \cap B^c } \right)}  \\<br />
   {} &  \Leftrightarrow  & {\left( {X\backslash A} \right) \cup \left( {X\backslash B} \right)}  \\<br /> <br />
 \end{array}
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