For any two subsets A and B of some set S,

$\displaystyle (A \cup B) - (A \cap B) = (A - B) \cup (B - A)$

where $\displaystyle X-Y = X \cap Y' $

Show that this is true by using a) Venn diagrams and b) algebraic manipulation using the properties of Boolean algebra.

Ok so im struggling to start on this. Part a i don't know how to start really. Part b I'm tempted to write

$\displaystyle X - Y = (X - Y')\cup(Y' - X)$

but doubt its right :/