2003 AMC 10A Question 6
AMC10 · 2003 AMC 10A
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 $x \ne y$