I have the following Boolean Algebra expression, shown below, and I'm at a loss as if it can actually be reduced further. I was thinking some kind of XOR but 3 input XOR gates aren't really what can be used here :S
$$X =(A\land B \land C) \lor (\neg A \land \neg B \land \neg C)$$
Can anyone help out here real quick?
Hint: You want to say $A,B,C$ are all the same (truth value). It is enough to say that $A = B$ and $B = C$. And you can quite easily say "$A = B$" using XOR and NOT, so the resulting expression would have just 2 XORs and 2 NOTs and 1 AND. That's the simplest solution I can think of using only AND, OR, NOT, XOR.