2003 AMC 10A Problem 6

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.