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.

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- Jun 28th 2010, 03:47 AMdunstaset 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. - Jun 28th 2010, 03:54 AMChris L T521
Yes, that's legal because $\displaystyle \cap$ is commutative ($\displaystyle A\cap B=B\cap A$) and associative ($\displaystyle (A\cap B)\cap C=A\cap(B\cap C)$).

Thus, you're correct in saying that

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

from which the desired result follows.

Does this make sense? - Jun 28th 2010, 04:09 AMdunsta
Thanks, i like to know I am doing things correctly and not just assuming I am.

I really appreciate your help and this forum!