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A relation R is defined on the set R+ of positive real numbers by a R b if the

Chapter 5, Problem 14

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QUESTION:

A relation R is defined on the set R+ of positive real numbers by a R b if the arithmetic mean (the average) of a and b equals the geometric mean of a and b, that is, if a+b 2 = ab. (a) Prove that R is an equivalence relation. (b) Describe the distinct equivalence classes resulting from R.

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QUESTION:

A relation R is defined on the set R+ of positive real numbers by a R b if the arithmetic mean (the average) of a and b equals the geometric mean of a and b, that is, if a+b 2 = ab. (a) Prove that R is an equivalence relation. (b) Describe the distinct equivalence classes resulting from R.

ANSWER:

Step 1 of 3

A relation  is an equivalence relation if and only if:

1. is reflexive

2. is symmetric

3. is transitive

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