1. The problem statement, all variables and given/known data Im looking at this example and trying to figure out how they showed it was associative. They start out with x*y=x+y+1 then they add in z to show it is associative. x*(y*z)=x*(y+z+1)=x+(y+z+1)+1=x+y+z+2 I dont know how they go from this x*(y+z+1)=x+(y+z+1)+1 and end up with the equation on the right. If i solved for x from x*y=x+y+1 and plugged it in I wouldn't get what they got. Maybe there is some trick that I am missing.