I'm having a very hard time simplifying this:
A!B!C+ABC+!A!BC+!AB!C
The objective here is to simplify the equation until it can be expressed in "AND"'s "OR"'s and "NOT"'s. I have to create an integrated circuit for the simplified expression using only those 3 gates in Logisim.
This is as far as I've gone:
A(!B!C+BC)+!A!BC+!AB!C
A+!A!BC+!AB!C
A+!BC+B!C
I'm not sure if this is right
If $!X$ means $1+X$ in the Boolean algebra then your expression simplifies to $A+B+C$. Check this by replacing the $!$ operators as indicated and distributing the multiplications. This expression can be written as
$$ (A \operatorname{AND} \operatorname{NOT} (B \operatorname{OR} C)) \operatorname{OR}\\ (B \operatorname{AND} \operatorname{NOT} (A \operatorname{OR} C)) \operatorname{OR}\\ (C \operatorname{AND} \operatorname{NOT} (A \operatorname{OR} B)) \operatorname{OR}\\ (A \operatorname{AND} B \operatorname{AND} C). $$
Note that $X+Y$ can be written as $(X \operatorname{OR} Y) \operatorname{AND} \operatorname{NOT} (X \operatorname{AND} Y)$.