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Let
a. Prove that “congruence modulo
” is an equivalence relation.
b. List five members of each of the equivalence classes
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Chapter 1 Solutions
ELEMENTS OF MODERN ALGEBRA
- 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.arrow_forward5. Let be the relation “congruence modulo ” defined on as follows: is congruent to modulo if and only if is a multiple of , we write . a. Prove that “congruence modulo ” is an equivalence relation. b. List five members of each of the equivalence classes and .arrow_forwardLet 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.arrow_forward
- True 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_forwardLabel 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_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
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