1. ## Simplifying a Set

Simplify the following using the set rules of interference.

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

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

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

Thanks!

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

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

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

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

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