trying to find associativity

Question

Is the binary operation define by: $x*Y = x+y-1$

what my tutor has done: $x*(y*z) = x *(y+z -1) = x+(y+z-1) = x+y+z-2$

My question: how did he get $x+y+z$-2

Where did the '-2' come from?

I am simply trying to learn how he did this, thanks guys.

Answer 1

There's a little mistake

$x*(y*z) = x *(y+z -1) = x+((y+z-1)\color{red}{-1}) = x+y+z-2$