1982 AMC 12 Question 7
AMC12 · 1982 AMC 12
If the operation $x*y$ is defined by $x*y=(x+1)(y+1)-1,$ then which one of the following is false?
$x*y=y*x$ for all real $x$ and $y.$
$x*(y+z)$ equals $(x*y)+(x*z)$ for all real
$x,$ $y,$ and $z.$
$(x-1)*(x+1)$ equals $(x*x)-1$ for all real $x.$
$x*0=x$ for all real $x.$
$x*(y*z)=(x*y)*z$ for all real $x,$ $y,$ and $z.$