Let R be a congruence relation modulo 7 on Z. Then the equivalence class [110] equals to which of the following: O [5] O 14] O [3] O [1] O [2] O o o o o
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![Let R be a congruence relation modulo 7 on Z. Then the equivalence class [110] equals to which of the following:
O [5]
O 14]
O [3]
O [1]
O [2]
O o o o o](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67b13aff-bfb5-4d63-8e56-0718b4a6f235%2Fe710da3c-eba5-4154-8e4d-b5091f752e04%2Fl32vioo_processed.png&w=3840&q=75)
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- 5. 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 .a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the equivalence class [ 3 ]. b. Let R be the equivalence relation congruence modulo 4 that is defined on Z in Example 4. For this R, list five members of equivalence class [ 7 ].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.
- In this exercise set, all variables are integers. 1. List the distinct congruence classes modulo , exhibiting at least three elements in each class.In this exercise set, all variables are integers. 2. Follow the instructions in Exercise for the congruence classes modulo . 1. List the distinct congruence classes modulo , exhibiting at least three elements in each class.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. If R is an equivalence relation on a nonempty set A, then any two equivalence classes of R contain the same number of element.15. Let be a binary operation on the non empty set . Prove that if contains an identity element with respect to , the identity element is unique.In Exercises 610, a relation R is defined on the set Z of all integers. In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and list at least four members of each. xRy if and only if x+3y is a multiple of 4.
- 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.True or False Label each of the following statements as either true or false. If is an equivalence relation on a nonempty set, then the distinct equivalence classes of form a partition of.Label each of the following statements as either true or false. The distinct congruence classes for congruence modulo n form a partition of .