he equivalence class of 3 for the relation congruence modulo 7 is given by O [7], = (..2,1,4,7,10,13...) O [3], = .,-23,-15,-7,1,8,8.16.,24... D [7], = .-2,0,5,9,11,14.. D [3],= { .....-18,-11,-4,3,10,17,24, .) %3D

Q: With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: (1) (a) Show that the relation a = b mod n if n | a – b is an equivalence relation (b) Show that the…

A:

Q: to show that the numbers in question are incongruent modulo n.] 11. Verify that 0, 1, 2, 22, 23,…

A: We shall solve this question in next step.

Q: The equivalence relation a = y(mod4) is defined on the set Z of integers. Determine the quotient…

A: The solution is below.

Q: A partition P of Z is said to be compatible with + if given any X, Y ∈ P and any x1, x2 ∈ X, y1, y2…

A: A partition P of ℤ is said to be compatible with + if given any X, Y ∈ P and any x1, x2∈X and…

Q: 26. Use Algorithm 1 to find the transitive closures of these relations on {a, b, c, d, e}. a) {(a,…

A:

Q: {0,1,2,3,4,5,6,7,8,9} by x ~y A x2 = is an equivalence relation on X and identify the equivalence…

A:

Q: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

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Q: Suppose (An'y is a nondecreasing Sequence of sets. Define the sequence of rondecrusing a monotone…

A:

Q: 4. Let S = {1, 2,..., 10}. Out of all the equivalence relations on S that have exactly 2 equivalence…

A:

Q: The equivalence class of -2 for the relation congruence modulo 5 is о (... -11, -6, —1,4, 9, 14,…

A: Second option is correct.

Q: 3. Let S be the congruent modulo 2 relation on Z, that is m S n 2|(m-n). Show the relation

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Q: 2. For each equivalence relation below, find the requested equivalence class. a. R = { (1,1), (1,…

A: As per our company guidelines we can solve only the first three subparts. Kindly re Post the other…

Q: 7. Decide for each of the following relations whether or not it is an equivalence relation. Give…

A: A relation is known as equivalence relatioon if it is reflexive, symmetric and transitive.

Q: 2. Suppose A = {1, 2, 3, 4, .. , 14, 15} and let R be the relation of congruence modulo 5 on the set…

A:

Q: Show that the number of equivalence relation in the set {1, 2, 3} containing(1, 2) and (2, 1) is…

A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

Q: The followings are 4 sequences which are represented by the first 6 elements. Which sequences can be…

A:

Q: Let S = {0, 1, 2, 4, 6}. Test the following binary relation on S for reflexivity, symmetry,…

A:

Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

A:

Q: The Modular class of [2] under modulo 8 is O [2] = {..., -8,-4,2,4,8,...} [2]={…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

Q: Determine whether the relation R on  the set of all people is reflexive,symmetric, antisymettric…

A: Consider the provide question,

Q: Define the relation∼ on Nby m ∼ n if and only if the sum of the distinct primes that divide m is the…

A: To test if the given relation satisfies the conditions for reflexivity, symmetry and transitivity

Q: Consider the congruence mod 6 for integers. Z6={[0], [1], [2], [3], [4], [5]}. Prove the product of…

A:

Q: The equivalence class of -1 for the relation congruence modulo 5 is O {...,-12, –7, –2, 3,8, 13,…

A:

Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

A:

Q: 6. If c is a positive integer and a and b are integers with a = b(mod c), show that a2 = b²(mod c).…

A: Let c is positive integers and  a and b are integers with a ≡ b ( mod c)

Q: 7. Let P be the congruence modulo 6 relation. Note, this is an equivalence relation. a. List 5…

A:

Q: Show that the relation R in the set A = {1, 2, 3, 4, 5} given byR = {(a, b) : |a – b| is even}, is…

A: Given that: A = {1, 2, 3, 4, 5} R = { (a,b) ; |a – b| is even}For any element a ∈A, we have |a -a| =…

Q: (a) Use cases based on congruence modulo 3 and properties of congruence to prove that for each…

A:

Q: (11) Let Z, denotes the integers (mod n), e.g., Z,, denotes the 10 equivalence classes Z1, = {[0],…

A:

Q: a. The relation x = y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

A:

Q: 5. Recall that Z stands for the equivalence classes of integers modulo n. We denote the congruence…

A:

Q: Consider the congruence mod 6 for integers. Z6={[0], [1], [2], [3], [4], [5]}. Prove the sum of an…

A:

Q: The partitions of the equivalence relation congruence modulo 4 is given by [0], [11, O [4],[4],[4],…

A: Here we have to find the partitions of the equivalence relation congruence modulo 4.

Q: Consider relation R={(1,1),(1,2),(2,1),(2,2),(3,3)} on the set{1,2,3}. R Is ? Select one: O a. Ris…

A: Let R be a relation defined as . The relation, R is reflexive, if , . The relation, R is…

Q: 3. Let S be the congruent modulo 2 relation on Z,that is m S n→ 2|(m-n) . Show the relation

A: A relation is called symmetric if for any  if  then we have .

Q: 3) Let S be the equivalence relation on P({0, 1, 2, 3}) defined by XSY if and only if ged(X], 4) =…

A:

Q: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

A: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

Q: Let A = {55, 63, 70, 83, 86, 106, 113, 116, 151} and R be an equivalence relation defined on A where…

A: Given : A=55, 63, 70, 83, 86, 106, 113, 116, 151 and R is an equivalence relation defined on A where…

Q: 3.3: Is brotherOf an equivalence relation on the set of all people?? How about siblingof?, same…

A:

Q: Consider congruence mod 5. Let r = {0, 1, 2, 3, 4}. 1) Find r so that 3 =r mod (5). 2) Find r so…

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Q: Show that for any n ∈ N that congruence mod n is an equivalence relation on the set of integers. How…

A:

Q: Prove that the relation of congruence modulo n is transitive. That is, prove that for all integers…

A:

Q: can a committee of 6 be 8. Use the binomial formula to expand the expression (2a2 - y)*. 9. In a…

A:

Q: Let R be the relation on the set N0 of natural numbers given by the following rule: (n,m)∈R(n,m)∈R…

A: Let R be the relation on the set N0 of natural numbers given by n,m∈R if and only if n-m is a…

Q: Determine which of the following congruence relations are true and which are false. (a) 47 = 3 (mod…

A:

Q: Partition (Z/19Z)* into equivalence classes determined by the identi- fication of elements of the…

A: According to the given information, it is required to determine the primitive roots modulo 19.