1. ## Simplifying a Set

Simplify the following using the set rules of interference.

$
[((A - B) \cup (A \cap C)) \cap (A \cap B)^C]^C
$

where A, B, and C are subsets of the Universe.

I've gotten it to $(A^C \cup (B \cap C^C)) \cup (A \cap B)$, but now I'm stuck.

Thanks!

2. Originally Posted by inferno
Simplify the following using the set rules of interference.

$
[((A - B) \cup (A \cap C)) \cap (A \cap B)^C]^C
$

where A, B, and C are subsets of the Universe.

I've gotten it to $(A^C \cup (B \cap C^C)) \cup (A \cap B)$, but now I'm stuck.

Thanks!
I am going to use the dash notation instead of the "c" natation,so:

$[((A - B) \cup (A \cap C)) \cap (A \cap B)^C]^C$ = $
[((A - B) \cup (A \cap C)) \cap (A \cap B)']'$
= $[((A - B) \cup (A \cap C))' \cup (A \cap B)]$

All you have to do now is to simplify $[((A - B) \cup (A \cap C))']$

3. xalk, thanks for your help. I realized that I needed to use the commutative and associative laws and then the absorption laws to arrive at an answer of an union of two subsets.