{0, 1, 2, 3, 4, ...} and define the relation - on A by: x~y if x – y is divisible by 3 Determine whether ~ is reflexive, symmetric and transitive.
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- 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 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.Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
- Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.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.For determine which of the following relations onare mappings from to, and justify your answer. b. d. f.