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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

1 solution

Andreas Wendler
Feb 14, 2016

The statement $x \heartsuit 0 = x$ is wrong for x<0. The others are true because they stand for properties of the absolute value function.

While -x+0 is -x and l-xl is x right? ist same with l-x+0l.. what the different?

Imam Edogawa - 5 years, 3 months ago