1. The problem is to simplify the expression $A - (B \cap C)$. 2. This expression represents the set difference between set $A$ and the intersection of sets $B$ and $C$. 3. The intersection $B \cap C$ contains all elements that are in both $B$ and $C$. 4. The set difference $A - (B \cap C)$ contains all elements that are in $A$ but not in $B \cap C$. 5. Using set theory rules, $A - (B \cap C) = A \cap (B \cap C)^c$, where $(B \cap C)^c$ is the complement of $B \cap C$. 6. By De Morgan's law, $(B \cap C)^c = B^c \cup C^c$. 7. Therefore, $A - (B \cap C) = A \cap (B^c \cup C^c)$. 8. Distributing $A$ over the union, we get $A \cap B^c \cup A \cap C^c$. 9. This means the elements are those in $A$ but not in $B$, or in $A$ but not in $C$. Final answer: $$A - (B \cap C) = (A - B) \cup (A - C)$$