5. Let R be a relation defined on Z by a Rb if and only if 3 | (a + 2b). (a) Prove that R is an equivalence relation. (b) Determine the equivalence class
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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.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.Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
- Let R be the relation defined on the set of integers by aRb if and only if ab. Prove or disprove that R is an equivalence relation.Label each of the following statements as either true or false. If R is an equivalence relation on a nonempty set A, then any two equivalence classes of R contain the same number of element.29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there is a subset such that . Prove that R is an equivalence relation on A and that the equivalence classes of R are the subsets .