# Math Help - Set operations

1. ## Set operations

for all sets, A B and C.

is this statement true?

(A - B) - C = A - (B - C)

2. Originally Posted by brudman
for all sets, A B and C.

is this statement true?

(A - B) - C = A - (B - C)
Note that $\left(A-B\right)-C=\left(A\cap B^{\prime}\right)\cap C^{\prime}$. Since we're dealing with intersections, we see that

\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 $\left(A-B\right)-C\neq A-\left(B-C\right)$ (this is reasonable, because "subtraction" isn't associative).

Does this make sense?

3. yes it does, thank you

4. BTW.
If I were your professor, I would expect you to give a counter-example.
That is the proper method of showing a statement is false.

5. This isn't a question from my professor, i just wanted to know if it is true or not