Set operations

**brudman** · November 15th 2009, 10:32 AM

for all sets, A B and C.

is this statement true?

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

**Chris L T521** · November 15th 2009, 10:43 AM

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?

**brudman** · November 15th 2009, 10:48 AM

yes it does, thank you

**Plato** · November 15th 2009, 12:29 PM

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.

**brudman** · November 15th 2009, 05:05 PM

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

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