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Algebra Level 2

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

Which of the following statements is not true?

x \heartsuit y > 0

if

x \not = y

x\heartsuit 0 = x

for all real x.

x\heartsuit y = y\heartsuit x

for all x and y.

x\heartsuit x = 0

for all real x.

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by Anish Harsha

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