MathDB

Define

x \heartsuit y

to be |x\minus{}y| for all real numbers

x

and

y

. Which of the following statements is not true?
(A)\ x \heartsuit y \equal{} y \heartsuit x \text{ for all } x \text{ and } y (B)\ 2(x \heartsuit y) \equal{} (2x) \heartsuit (2y) \text{ for all } x \text{ and } y (C)\ x \heartsuit 0 \equal{} x \text{ for all } x (D)\ x \heartsuit x \equal{} 0 \text{ for all } x

<span class='latex-bold'>(E)</span>\ x \heartsuit y > 0 \text{ if } x \ne y

Problem Statement