Let R = {(a, b) | a = b (mod 3)} be an equivalence relation on the set of integers Z.What are the three equivalence classes of R? Provide five integers that are members of each equivalence class.

Answered: Image /qna-images/answer/c497975c-06b0-422f-ac18-fdf7a5e3ead4.jpg

Answered: Let R = {(a, b) | a = b (mod 3)} be an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

???
Consider the set S = {A, B, C, D}: For each of the following relations on S, determine whether it is a partial order, a total order, an equivalence relation, or none of the above, and in one sentence explain why: a) {(A,B), (B,C), (C,D), (A,C), (B,D), (A,D)} b) {(A,A), (B,A), (B,B), (C,C), (C,D), (D,D)} c) {(A,A), (B,A), (A,B), (B,B), (C,C), (A,C), (C,A), (D,D)} d) {(A,A), (B,A), (A,B), (B,B), (C,C), (D,D)} e) {(A,A), (B,A), (A,B), (B,B), (C,C), (C,D), (D,D)}
Answer the questions a) How many binary relations exist on an empty set? b)
Let [n] denote the set of integers {1, 2, . , n). How many ways are there to permute the elements of the set [7] so that there is an even number in the first place?
Define the following relation R in the set X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. For integers x, y ∈ X, let xRy if and only if x^2 - y^2 or x^2 + y^2 is divisible by 10. Prove that R is an equivalence relation and determine the equivalence classes of R.
2 DO NOT COPY FROM OTHER WEBSITES
Define - on Z as follows. Suppose that a ~ b if a² = b² (mod 6). Prove that - is an equivalence relation.
Subject : Calculas
Show that the relation R defined on the set of integers ℤ by (a,b) ∈ R if a – b = 6k for some k ∈ ℤ is an equivalence relation.
3. Prove that a = b(mod7)is an equivalence relation by taking suitable examples.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Let R = {(a, b) | a = b (mod 3)} be an equivalence relation on the set of integers Z. What are the three equivalence classes of R? Provide five integers that are members of each equivalence class.