4|(x+3y)
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Define a relation R on Z as xRy if and only if 4|(x+3y). Answer the following questions. Show your work in sufficient detail.
- Prove R is an equivalence relation.
- Describe its equivalence classes.
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- 23. Let be the equivalence relation on defined by if and only if there exists an element in such that .If , find , the equivalence class containing.Label each of the following statements as either true or false. Every mapping on a nonempty set A is a relation.Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.