Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in general, that is, prove that if A is a nonempty set, and P is a partition of A, then the relation R corresponding to P defined in (*) must be an equivalence relation.

(b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in general, that is, prove that if A is a nonempty set, and P is a partition of A, then the relation R corresponding to P defined in (*) must be an equivalence relation.

Advanced Engineering Mathematics
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
icon
Related questions
Question

I just need answer for ii

*18. Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A by X. x Ry if there exists S E P such that x, y E S. (*) (a) Let A = {1, 2,3}. Write down ALL possible partitions of A. For each of the partition P, use (*) to write down the relation R (as a subset of A x A) corresponding to P. (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in general, that is, prove that if A is a nonempty set, and P is a partition of A, then the relation R corresponding to P defined in (*) must be an equivalence relation.
Transcribed Image Text:*18. Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A by X. x Ry if there exists S E P such that x, y E S. (*) (a) Let A = {1, 2,3}. Write down ALL possible partitions of A. For each of the partition P, use (*) to write down the relation R (as a subset of A x A) corresponding to P. (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in general, that is, prove that if A is a nonempty set, and P is a partition of A, then the relation R corresponding to P defined in (*) must be an equivalence relation.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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,
SEE MORE TEXTBOOKS