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What is wrong with the following argument, which purports to prove that a binary relation that is symmetric and transitive must necessarily be reflexive as well?
Suppose R is a symmetric and transitive relation on a set A and let
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Discrete Mathematics with Graph Theory
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- Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.arrow_forwardLet 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.arrow_forwardTrue or False Label each of the following statements as either true or false. Let be an equivalence relation on a nonempty setand let and be in. If, then.arrow_forward
- 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.arrow_forwardLabel 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.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
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