law of sets algebra

[solomon_13000]

proof:

A - (B u C) = (A - B) n (A - C)

my solution:

x E A and x E - (B u C)

x E A and x E (B or C)`

x E A and x E (`B and `C)

x E (A - B) n (A - C)

this means A - (B u C) = (A - B) n (A - C)

Is this correct?

 

[pka]

You have done it by "pick a point".
Here is another way.
\(\displaystyle \L \begin{array}{rcl}
A - \left( {B \cup C} \right) & = & A \cap \left( {B \cup C} \right)' \\
& = & A \cap \left( {B' \cap C'} \right) \\
& = & \left( {A \cap B'} \right) \cap \left( {A \cap C'} \right) \\
& = & \left( {A - B} \right) \cap \left( {A - C} \right) \\
\end{array}.\)