# Math Help - set intersection

1. ## 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

2. $\begin{array}{l}
= \left( {A \cup B} \right) \cap \left( {B \cup C} \right)^\prime \cap \left( {A \cup C} \right)^\prime \\
= \left( {A \cup B} \right) \cap \left[ {\left( {B \cup C} \right) \cup \left( {A \cup C} \right)} \right]^\prime \\
= \left( {A \cup B} \right) \cap \left[ {\left( {A \cup B \cup C} \right)} \right]^\prime \\
= \emptyset \\
\end{array}$