# Math Help - set property help

1. ## set property help

Am I correct in assuming:

using A-B = AnB'

(A-B)-C = (A-C)-B
(AnB') - C
(AnB')nC'
AnB'nC'
AnC'nB' <- is this legal?
(A-C)nB'
= (A-C)-B

Thanks for any help.

2. Originally Posted by dunsta
Am I correct in assuming:

using A-B = AnB'

(A-B)-C = (A-C)-B
(AnB') - C
(AnB')nC'
AnB'nC'
AnC'nB' <- is this legal?
(A-C)nB'
= (A-C)-B

Thanks for any help.
Yes, that's legal because $\cap$ is commutative ( $A\cap B=B\cap A$) and associative ( $(A\cap B)\cap C=A\cap(B\cap C)$).

Thus, you're correct in saying that

\begin{aligned}A\cap B^{\prime}\cap C^{\prime}&=A\cap(B^{\prime}\cap C^{\prime})\\ &= A\cap(C^{\prime}\cap B^{\prime})\\ &=(A\cap C^{\prime})\cap B^{\prime}\end{aligned}

from which the desired result follows.

Does this make sense?

3. Thanks, i like to know I am doing things correctly and not just assuming I am.
I really appreciate your help and this forum!