
laws of set algebra
i am having a bit(actually alot) of problems with set algebra
here are some examples
using laws of set algebra show that generally
(x\y) u (x n y) = x
heres another one
(y'\x) 'u (x \ y) = x u y
can you please explain in detail (i am clueless bout these questions)
how you solved them, the explanation is more important than the answer, i have a test soon so a quick replay would be helpfull

$\displaystyle X\backslash Y = X \cap Y^c $
$\displaystyle \begin{array}{rcl} \left( {X\backslash Y} \right) \cup \left( {X \cap Y} \right) & = & \left( {X \cap Y^c } \right) \cup \left( {X \cap Y} \right) \\
& = & X \cap \left( {Y^c \cup Y} \right) \\
& = & X \\ \end{array}
$

i didnt really want the answer just an explanation of how set algebra is applied in these equations