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Let R denote the set of nonzero real numbers. Define a relation R on R by a R b if ab >
Chapter 5, Problem 6(choose chapter or problem)
Let R denote the set of nonzero real numbers. Define a relation R on R by a R b if ab > 0. (a) Determine whether R is an equivalence relation. (b) If R is an equivalence relation, then describe the distinct equivalence classes.
Questions & Answers
QUESTION:
Let R denote the set of nonzero real numbers. Define a relation R on R by a R b if ab > 0. (a) Determine whether R is an equivalence relation. (b) If R is an equivalence relation, then describe the distinct equivalence classes.
ANSWER:Step 1 of 3
A relation is said to be equivalence relation on a set , then it satisfies the following properties.
* Reflexive: If for all ; that is, if , then ;
* Symmetric: if whenever , then for all ; that is, if , then ;
* Transitive: if whenever and , then for all ; that is, if and , then.