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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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