# Problem #2082

 2082 Define $x \heartsuit y$ to be $|x-y|$ for all real numbers $x$ and $y$. Which of the following statements is not true? $\mathrm{(A) \ } x \heartsuit y = y \heartsuit x$ for all $x$ and $y$ $\mathrm{(B) \ } 2(x \heartsuit y) = (2x) \heartsuit (2y)$ for all $x$ and $y$ $\mathrm{(C) \ } x \heartsuit 0 = x$ for all $x$ $\mathrm{(D) \ } x \heartsuit x = 0$ for all $x$ $\mathrm{(E) \ } x \heartsuit y > 0$ if $x \neq y$ This problem is copyrighted by the American Mathematics Competitions.
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