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Math Help - set intersection

  1. #1
    Junior Member
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    set intersection

    if a,b,c are arbitraty sets, shows that

    [(a u B ) - (b U C) ]intersect ( A u C) ' = null

    my steps


    [ (a u b) intersect ( b u c )' ]intersect (A u c )'

    [ ( a u b ) intersect ( b' intersect c') ] intersect ( A u c)'

    [ ( a u b ) intersect b' ( a u b ) intersect c' ] intersect ( a u c )'


    STUCK at here. dont knw to continue


    edit*[(a u B ) - (b U C) ]intersect ( A u C) ' = null <---------got [ ] inside
    Last edited by qweiop90; July 16th 2008 at 09:12 AM.
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  2. #2
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    \begin{array}{l}<br />
  = \left( {A \cup B} \right) \cap \left( {B \cup C} \right)^\prime   \cap \left( {A \cup C} \right)^\prime   \\ <br />
  = \left( {A \cup B} \right) \cap \left[ {\left( {B \cup C} \right) \cup \left( {A \cup C} \right)} \right]^\prime   \\ <br />
  = \left( {A \cup B} \right) \cap \left[ {\left( {A \cup B \cup C} \right)} \right]^\prime   \\ <br />
  = \emptyset  \\ <br />
 \end{array}
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