5. Consider the relation in N given by n~m if n and m have the same number of digits in the decimal representation. Is this an equivalence relation? If so find a partition of N in the corresponding classes of equivalence.

Q: {k}, {I, m, o}, {n, p}} of the set U = {k, I, m, n, o, p}. Give the

A: Solution is attached below.

Q: Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an…

A: Equivalence classes: Let A be a nonempty set. Let R be the equivalence relation defined on A. Let…

Q: Let A = {74, 77, 83, 89, 92, 112, 119, 134, 148} and R be an equivalence relation defined on A where…

A: Given A={74,77,83,89,92,112,119,134,148} For a∈A  class of a=[a]={x∈A : xRa }={ x∈A : x≡a mod 5 } ={…

Q: Define a relation = on Zby m = n if m – n is divisible by 3. a. Show that is an equivalence…

A:

Q: For any binary relation ▷ on a set X, define the binary relation by letting xy we do not have ▷y.…

A: Given that ⊳ is a binary relation on a set X. Now define a relation ⊳ as follows: x⊳y if and only if…

Q: Prove that R is symmetric

A:

Q: 6. Let A = {a, b, c, d, e}. Define a relation Ron P(A} by BRC if|B| = |C]. B is related to Cif they…

A:

Q: (c) For the partial order you identified above, is every pair of elements of Z comparable? (You…

A:

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

A:

Q: Let D be the set of digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Define a relation R on the power set P(D)…

A: Dear Student,   As per our guidelines we can answer only first three subqustions. So kindly resubmit…

Q: 10. (A is the relation defined on Z as follows: for all x, y = Z, x Ay ⇒x=y (mod 3). Describe the…

A:

Q: 1. Let R be the relation on Z defined by a) b) mRn if and only if mn > 0 or m = n = 0. Prove that R…

A:

Q: a. Recall that the set Z of integers is the set of equivalence classes {[(a, 6)] | a, 8 e N}, where…

A:

Q: 1. Consider the relation R on the set A = {0,1, 2, 3, 4}, defined by: %3D aRb + a = bc and b= ad,…

A: The given set is A=0,1,2,3,4 and the relation is defined as aRb⇔a=bc and b=ad (a) Check whether R an…

Q: For a positive integer n ≥ 4, let {0, 1]" denote the set of all binary strings of length n. The…

A: For a positive integer n≥4, let 0,1n denote the set of all binary strings of length n. Observe that,…

Q: 6. Consider the relation R on Z defined by xRy iff x – y= 4n for some n Ɛ Z. (a) Show that R is an…

A:

Q: (3) In each item below, verify that - is an equivalence relation on the given set. (c) Let - be a…

A:

Q: Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an…

A:

Q: 5. Let A = {41, 49, 67, 71, 73, 76, 81, 88, 111} and R be an equivalence relation defined on A where…

A:

Q: 7.5.14. Consider the equivalence relation congruence mod 5, on the set of integers. (a) Describe the…

A:

Q: 30. Let S= {1,2,3} and let R be an equivalence relation on S. (a) Describe the R with the fewest…

A:

Q: 6. Consider the partition P = {{0}, {-1,1}, {-2,2}, {-3,3},{-4,4},...} of Z. Describe the…

A: Given the partition of Z is P=0,-1,1,-2,2,-3,3,-4,4,....

Q: To submit For each positive integer n, define the set A, = {2'(2n – 1) : ieZzo}. (a) Prove that P =…

A: Given, An=2i2n-1:i∈ℤ≥0 Part(a): Let,…

Q: 2. Suppose I wish to define a function g : {0, 1, 2, 3, 4} → Z that takes an input of an equivalence…

A:

Q: Discrete Math: Let X  be the set of real numbers. Assume that R on X is an equivalence relation.…

A: X is the set of real numbers and R is an equivalence relation on X.The question asks if a partition…

Q: For each a, let Aa = {(x, y) E R² | x² + y = a}. Prove that U A. is a partition aɛR of R?. Describe…

A:

Q: 6. Find all elements of the equivalence class of 12 under congruence modulo 5.

A: Given : 12 mod 5. To Find : All element of equivalence class of 12 under congruence modulo 5 . " As…

Q: Let S be the set of all strings of length 4 of letters in the set A = { a, b, c, d, e, f }…

A:

Q: Let A = {1,2,3,4,5} B= (6,7,8,9} Define an equivalence relation of p in A UB with atleast 12 members

A: A=1,2,3,4,5B=6,7,8,9A∪B=1,2,3,4,5,6,7,8,9

Q: Let A = {43, 44, 57, 67, 80, 97, 107, 109, 121} and R be an equivalence relation defined on A where…

A: Introduction: To find the partition of A defined by the equivalence classes of R, we need to find…

Q: Consider the following binary relation: Vx, y E R?, x Ey if x1 > Yı (indepen- dent of x2 and y2) or…

A: We will use the basic knowledge of relations to answer this question correctly and completely.…

Q: (b) Consider the finite set A = equivalence classes that S partitions the set A into. {1,2,3,,,,,).…

A: Solution To draw the graphical representation of the equivalence relation \( S \) on set \( A \), we…

Q: a) How many binary relations exist on an empty set

A: To find: number of binary relation on given set. Please post the multiple questions separately. Here…

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

A: