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A relation R is defined on the set Z of integers by a R b if 11a 5b is even. (a) Show
Chapter 5, Problem 9(choose chapter or problem)
QUESTION:
A relation R is defined on the set Z of integers by a R b if 11a 5b is even. (a) Show that R is an equivalence relation. (b) Describe the distinct equivalence classes resulting from R. 1
Questions & Answers
QUESTION:
A relation R is defined on the set Z of integers by a R b if 11a 5b is even. (a) Show that R is an equivalence relation. (b) Describe the distinct equivalence classes resulting from R. 1
ANSWER:Step 1 of 3
The following properties are used for checking a relation is said to be an equivalence relation on a set .
* 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.