Solution Found!
A relation R is defined on the set R+ of positive real numbers by a R b if the
Chapter 5, Problem 14(choose chapter or problem)
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.
Questions & Answers
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