Prove that the following relations are equivalenece relations and identify equivalence classes: 1. On R, x y, if x y is an integer. 2. On R 2 ,(x1, y1) (x2, y2) if x1 = x2. 3. On R 2 {(0, 0)},(x1, y1) (x2, y2) if there exists a R, a 6= 0, such that x1 = ax2 and y1 = ay2.

83 Views

Prove that the following relations are equivalenece relations and identify equivalence classes: 1. On R, x y, if x y is an integer. 2. On R 2 ,(x1, y1) (x2, y2) if x1 = x2. 3. On R 2 {(0, 0)},(x1, y1) (x2, y2) if there exists a R, a 6= 0, such that x1 = ax2 and y1 = ay2.

Akash Girde 7th Nov, 2020

Answer

Answer Later

Report

Answer (1)

Anuj More 7th Nov, 2020

Dear Akash,

What you are asking is to prove a mathematical statement. Kindly note this is not possible on this platform as we are limited by our answering ways. You may search this query on internet and you may find various portals which may help you understand your query.

Hope this helps. Thanks.

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.

94 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].

122 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.

116 Views

For x,y ∈ R def i ne x ∼ y to mean that |x| = |y|. Prove that ∼ is an equivalence relation in R. Describe [0],[5], and [−5].

342 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

76 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

UPES Integrated LLB Admission...

Apply

Ranked #28 amongst Institutions in India by NIRF | Ranked #1 in India for Academic Reputation by QS University Rankings | 16.6 LPA Highest CTC

Great Lakes PGPM & PGDM 2025

Apply

Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024 | Extended Application Deadline: 10th Jan 2024

Amity University Noida B.Tech...

Apply

Among Top 30 National Universities for Engineering (NIRF 2024)

ISBR Business School PGDM Adm...

Apply

250+ Companies | Highest CTC 16 LPA | Average CTC 8 LPA | Ranked as Platinum Institute by AICTE for 6 years in a row | Awarded Best Business School...

Chandigarh University Admissi...

Apply

Ranked #1 Among all Private Indian Universities in QS Asia Rankings 2025 | Scholarships worth 210 CR

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