Let X = R. For n Z, let An = {x R : n x < n + 1} = [n, n + 1). 1. Prove that P = {An : n Z} is a partition of R. 2. Define an equivalence relation on R for which equivalence classes are {An; n Z}.

34 Views

Let X = R. For n Z, let An = {x R : n x < n + 1} = [n, n + 1). 1. Prove that P = {An : n Z} is a partition of R. 2. Define an equivalence relation on R for which equivalence classes are {An; n Z}.

Akash Girde 7th Nov, 2020

Answer

Answer Later

Report

Answer (1)

Anuj More 8th Nov, 2020

Dear Candidate,

You have asked us to prove a mathematical statement. We are limited by our answering options. You can search this question on various portals on the internet if you wish to have an answer based on your query. It is difficult for us to answer your query because of our limitations.

Thanks. Hope you understand.

Like Share

Related Questions

For x, y R define x y to mean that x y Z. 1. Prove that is an equivalence relation on R. 2. List three real numbers x such that x 2.

108 Views

For a, b belongs to R define xRy to mean that x-y belongs to Z. (1) Prove that Relation is an equivalence relation on R. (2) List three real numbers x such that x related to square root 2

89 Views

Problem 1.4. For x,y ∈ R def i ne x ∼ y to mean that x − y ∈ Z. 1)Prove that ∼ is an equivalence relation on R. 2)List three real numbers x such that x ∼ √2.

125 Views

For x, y R define x y to mean that |x| = |y|. Prove that is an equivalence relation in R. Describe [0], [5], and [5].

141 Views

Let M(n, R) denote the set of all n × n matrices over R. Define a relation on M(n, R) as follows: for A, B M(n, R), A B iff there exists an invertible matrix P such that P 1AP = B. Show that is an equivalence relation.

176 Views

Applications for Admissions are open.

Amity University, Noida Law A...

Apply

700+ Campus placements at top national and global law firms, corporates and judiciaries

Amity University, Noida BBA A...

Apply

Ranked amongst top 3% universities globally (QS Rankings)

VIT Bhopal University | M.Tec...

Apply

M.Tech admissions open @ VIT Bhopal University | Highest CTC 52 LPA | Apply now

Amity University | M.Tech Adm...

Apply

Ranked amongst top 3% universities globally (QS Rankings).

Graphic Era (Deemed to be Uni...

Apply

NAAC A+ Grade | Among top 100 universities of India (NIRF 2024) | 40 crore+ scholarships distributed

Great Lakes PGPM & PGDM Admis...

Apply

Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024

View All Application Forms

Trending Articles/News

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students

30,000+ Colleges

500+ Exams

1500+ E-books