Define a relation R on Z by declaring that xRy if and only if x^2 ≡ y^2 (mod 3). (a) Prove that R is an equivalence relation. (b) Find the equivalence classes [0] and [1]. (c) Determine if 0 or 1 is in the equivalence class [2022].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

 Define a relation R on Z by declaring that xRy if and only if x^2 ≡ y^2 (mod 3).

(a) Prove that R is an equivalence relation.

(b) Find the equivalence classes [0] and [1].

(c) Determine if 0 or 1 is in the equivalence class [2022].

(a) Prove that R is an equivalence relation.
(b) How many distinct equivalence classes are there for R?
(c) Find the smallest positive integer n such that [2022] = [n].
Transcribed Image Text:(a) Prove that R is an equivalence relation. (b) How many distinct equivalence classes are there for R? (c) Find the smallest positive integer n such that [2022] = [n].
Define a relation R on Z by declaring that xRy if and only if x² = y? (mod 3).
Transcribed Image Text:Define a relation R on Z by declaring that xRy if and only if x² = y? (mod 3).
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,