X Loves Y

Algebra Level 3

Define $x \heartsuit y = |x-y|$ for all real numbers $x$ and $y$ .

Which of the following statements is not true?

x\heartsuit x = 0

for all real x.

x\heartsuit 0 = x

for all real x.

x\heartsuit y = y\heartsuit x

for all x and y.

x \heartsuit y > 0

x \not = y