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Beyond Horizon Set 1 Paper 2 · Q12

Paper 2Logic & proof

Define x♡yx\heartsuit y to be ∣x−y∣|x-y| for all real numbers xx and yy. Which of the following statements is not true?

Ax♡y=y♡xx\heartsuit y=y\heartsuit x for all xx and yy
B2(x♡y)=(2x)♡(2y)2(x\heartsuit y)=(2x)\heartsuit(2y) for all xx and yy
Cx♡0=xx\heartsuit 0=x for all xx
Dx♡x=0x\heartsuit x=0 for all xx
Ex♡y>0x\heartsuit y>0 if x≠yx\ne y

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