# Distributive/Associative Law Q

• Dec 16th 2012, 02:20 PM
DirectorRico
Distributive/Associative Law Q
If I am trying to prove this:

For all sets A,B,C
(A intersection B)\C = (A\C) intersection (B\C)

If I start with proving X is a subset of Y (L.S. = R.S.), could I do the following?
(xeA ^ xeB) ^ (x/e/C)
Then using distributive law...
(xeA ^ x/e/C) ^ (xeB ^ x/e/C) <=> (A\C) intersection (B\C)

And then for Y is a subset of X...
Use the same distributive rule (backwards)

I'm wondering if this is a justified proof? If not, what would be the correct approach?

Thanks
• Dec 16th 2012, 02:45 PM
Plato
Re: Distributive/Associative Law Q
Quote:

Originally Posted by DirectorRico
If I am trying to prove this:
For all sets A,B,C
(A intersection B)\C = (A\C) intersection (B\C)

\displaystyle \begin{align*}(A\cap B)\setminus C&= (A\cap B)\cap C^c\\ &=(A\cap C^c)\cap (B\cap C^c) \\ &=(A\setminus C)\cap(B \setminus C) \end{align*}.
• Dec 16th 2012, 02:49 PM
DirectorRico
Re: Distributive/Associative Law Q
Great! Thanks Plato. +rep