How to use xor properly I need to know how to use XOR properly on more than two variables.
I have following example.
a xor b xor c
Now, the way I understand it is that:
$a$ xor $b$ = $a$ * not $b$ + not $a$ * $b$
That part is fairly simple for me to understand but how does the next part work? I imagine it goes like this.
($a$ * not $b$ + not $a$ * $b$) xor $c$
So, how can I use XOR on more than one variable?

NOTE: Just so you know, a XOR b is the same as $a \oplus b$. Also, here's a shortcut to XOR: If $a$ and $b$ are different, then $a \oplus b=1$. Otherwise, if they're the same, $a \oplus b=0$. Your formula works as a definition for XOR, but when you're calculating XOR in your head, I think this rule of thumb is easier.
If you know how to calculate $a \oplus b$, then you can simply calculate $a \oplus b$, set that to $d$ and then calculate $d \oplus c$. Basically, you work with two elements at a time: First, you look at the first two elements and then you take that result and use it with the third element.
Here's an example: Calculate $1 \oplus 0 \oplus 1$. Since $1$ and $0$ are different, we know that $1 \oplus 0=1$. This means that we now need to figure out $1 \oplus 1$. The first $1$ comes from the result of our first $\oplus$ calculation and the second $1$ comes from the fact that $1$ was the third element in our original expression. Since $1$ and $1$ are the same, we know that $1 \oplus 1=0$. Thus, $1 \oplus 0 \oplus 1=0$.
