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1982 AMC 12 Question 7

AMC12 · 1982 AMC 12

Question 7

If the operation $x*y$ is defined by $x*y=(x+1)(y+1)-1,$ then which one of the following is false?
  1. $x*y=y*x$ for all real $x$ and $y.$
  2. $x*(y+z)$ equals $(x*y)+(x*z)$ for all real
    $x,$ $y,$ and $z.$
  3. $(x-1)*(x+1)$ equals $(x*x)-1$ for all real $x.$
  4. $x*0=x$ for all real $x.$
  5. $x*(y*z)=(x*y)*z$ for all real $x,$ $y,$ and $z.$