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?