for all sets, A B and C.
is this statement true?
(A - B) - C = A - (B - C)
Note that $\displaystyle \left(A-B\right)-C=\left(A\cap B^{\prime}\right)\cap C^{\prime}$. Since we're dealing with intersections, we see that
$\displaystyle \begin{aligned}\left(A\cap B^{\prime}\right)\cap C^{\prime}&=A\cap\left(B^{\prime}\cap C^{\prime}\right)\\ &= A-\left(B^{\prime}-C\right)\end{aligned}$
So it appears that $\displaystyle \left(A-B\right)-C\neq A-\left(B-C\right)$ (this is reasonable, because "subtraction" isn't associative).
Does this make sense?