2003 AMC 12A Question 6
AMC12 · 2003 AMC 12A
Define $x\heartsuit y$ to be $|x - y|$ for all real numbers $x$ and $y.$ Which of the following statements is *not* true?
$x\heartsuit y = y\heartsuit x$ for all $x$ and $y$
$2(x\heartsuit y) = (2x)\heartsuit(2y)$ for all $x$ and
$y$
$x\heartsuit 0 = x$ for all $x$
$x\heartsuit x = 0$ for all $x$
$x\heartsuit y \gt 0$ if $x \neq y$