9. What are the congruence classes [0 ]5 , [3 ]5, [4]5 in the set of integers?

Q: Write a complete residue system modulo 13 consisting only of odd integers.

A:

Q: Construct the Addition Table of Congruence Class Z5.

A: The number of elements of the given group is written as: ℤ5=0,1,2,3,46=1=−45=0,6=1,7=2 and 8=3and if…

Q: +3 + 32 +.+3" 2 = 4"

A:

Q: what

A:

Q: What does the K stand for in Kn? (Finite)

A:

Q: 1. Find all cquivalent classes determined by congruence modulo 5 on Z.

A: The equivalent classes under modulo n is defined by, a=x∈ℤ: x≡amod nIn the question n=5a=x∈ℤ: x≡amod…

Q: How many equivalence relations on A=|42| are there that have distinct equivalence classes of size 4,…

A: Given A=|42| and distinct equivalence classes of sizes 4, 7,7, 8,8, and 8.

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

A:

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

A:

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

A:

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

A:

Q: ,1), (2, 2), (1, 3), (4, 1), (3, 2), (2, 3), (1,4), (5, 1), .... Show that this constitutes a proof…

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

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: 1. Consider the following rules on the set of natural numbers, N, 1) write down 5 ordered pairs of…

A: The 5 order pair of the natural number that is satisfy the relation “less than or equal to” as…

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: 2. Use a Venn diagram to illustrate the subset of odd integers in the set of all positive integers…

A:

Q: Suppose A = {-4,-3,–2,–1,0,1,2,3,4} and R is defined on A by aRb a² - b² is divisible by 4. Prove…

A: A relation R on a set A is said to be an equivalence relation, if it satisfies the following three…

Q: Let n, m, a, b be positive integers. motl Lof oontredietion u th

A: Given, n, m, a, b be positive integers. To prove that…

Q: A binary operation * on a set of integers is defined as x*y = x^2 + y^2. Which one of the following…

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: Suppose there is a currency which only uses 3-cent coins and 7-cent coins. Prove that for all…

A:

Q: Give a recursive definition for the set of all binary palindromes, that only '0's and 'l's that are…

A:

Q: п(п + 1) Show that , k 2 k=1

A:

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

A:

Q: (A) Compute the (infinite) discrete convolution (-2, –5, –3, –1) • (–4, –4, –5, –4).

A: Use the sum by column method to calculate the discrete convolution .                 Disclaimer:…

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

A:

Q: Show that the set of Galassaian integers x:X = atib , asb€ Th} set of integersy with unit Xing the…

A: We have the given set is S=x:x=a+ib, a,b∈Z where Z is the set of integers. First we prove that S is…

Q: Prove that if n, k are positive integers with k | (n +4) and k| (n – 1), then either k = 1 or k = 5.…

A: k | (n+4)  k | (n-1)  => k | {(n+4) - (n-1)} => k | 5

Q: Consider the set Q = Z ×(Z 10), and the relation tupon QDefined as: (a, b) ↑ (c, d) a•d = b•c d)…

A: Answer is mentioned below

Q: When we work with a congruence class, we have to keep two key things in mind. First, we have to know…

A: For ℤ3, The ones that are congruent to 0 is the set {...,-6,-3,0,3,6,..}. We call it the congruence…

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: There are 17 distinct congruence classes modulo 19. True False

A: we know that from the property of congruence classes    There are exactly n distinct congruence…

Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

A:

Q: Suppose n > 3 is an integer. Prove that in Sn every even permutation is a product of cycles of…

A:

Q: If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which…

A: The number of r combinations which can be selected from n numbers if repetitions allowed is…

Q: Prove that: there exist infinitely many 5-tuples of practical numbers of the form (n-8, n – 4, n,…

A: It is given that 5-tuples of practical number of the form (n-8, n-4, n, n+4, n+8)

Q: Compute the lattice of sub-extensions in the extension Q(C12)/Q

A: Consider the provided question,

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

A:

Q: Find an increasing subsequence of maximal length and a decreasing subsequence of maximal length in…

A: GIVEN CLEAR EXPLANATION BELOW

Q: What is the correct answer to "There are as many equivalence classes as there are which of the…

A: There are many equivalence classes.

Q: Prove that if n > 1 is a number with φ(n) = n/k, then k = 2,3.

A:

Q: 2) Let A be the set of all integers. Suppose that xRy + x and y have the same reminder when divided…

A:

Q: Give an example of a pair of numbers that can be used to generate modulo residues to represent the…

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.

Q: Prove that (1 -)(1-÷)(1-→).--(-) for all integers m 2 2 by m 2m nathematical induction.

A: *concept:- formula, a^2 - b^2 = (a+b)*(a-b).

Q: If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which…

A: As we know that any truples h,i,j,k,m with n≥h≥i≥j≥k≥m≥1  can be represented as a string of n-1…

Q: Compute: gcd(51, 42) Find a pair of integers x and y such that 51x + 42y = gcd(51, 42) (x, y) = (…

A: