In each of 7-14, relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R. A = { − 5 , − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4 , 5 } R is defined on A as follows: For all m , n ∈ Z .

m R n ⇔ 3 ( m 2 − n 2 ) .

To determine

To find the distinct equivalence classes of R.

Explanation

Given information:

The relation R is an equivalence relation on the set A.

A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}. R defined on A as follows: For all m,n∈Z,

m R n ⇔ 3|(m2−n2).

Calculation:

A={−5,−4,−3,−2,−1,0,1,2,3,4,5}R={(a,b)∈A×A|3|( a 2 − b 2 )}

Let us first determine the values are in the same equivalence class as − 5. A is in the same equivalence class as − 5, when (−5,a)∈R and thus when (−5)2−a2=25−a2 is divisible by 3 (( −5)2−a2=25−a2 is a multiply of 3).

Element (−5)2−a2=25−a2 in same equivalence class as − 5

− 4 25 − (- 4)2 = 25 − 16 = 9 Yes

− 3 25 − (- 3)2 = 25 − 9 = 16 No

− 2 25 − (- 2)2 = 25 − 4 = 21 Yes

− 1 25 − (- 1)2 = 25 − 1 = 24 Yes

0 25 − 0² = 25 − 0 = 25 &e

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Sect-8.1 P-1TY Sect-8.1 P-2TY Sect-8.1 P-3TY Sect-8.1 P-4TY Sect-8.1 P-5TY Sect-8.1 P-1ES Sect-8.1 P-2ES Sect-8.1 P-3ES Sect-8.1 P-4ES Sect-8.1 P-5ES

Sect-8.1 P-6ES Sect-8.1 P-7ES Sect-8.1 P-8ES Sect-8.1 P-9ES Sect-8.1 P-10ES Sect-8.1 P-11ES Sect-8.1 P-12ES Sect-8.1 P-13ES Sect-8.1 P-14ES Sect-8.1 P-15ES Sect-8.1 P-16ES Sect-8.1 P-17ES Sect-8.1 P-18ES Sect-8.1 P-19ES Sect-8.1 P-20ES Sect-8.1 P-21ES Sect-8.1 P-22ES Sect-8.1 P-23ES Sect-8.1 P-24ES Sect-8.2 P-1TY Sect-8.2 P-2TY Sect-8.2 P-3TY Sect-8.2 P-4TY Sect-8.2 P-5TY Sect-8.2 P-6TY Sect-8.2 P-7TY Sect-8.2 P-8TY Sect-8.2 P-9TY Sect-8.2 P-10TY Sect-8.2 P-1ES Sect-8.2 P-2ES Sect-8.2 P-3ES Sect-8.2 P-4ES Sect-8.2 P-5ES Sect-8.2 P-6ES Sect-8.2 P-7ES Sect-8.2 P-8ES Sect-8.2 P-9ES Sect-8.2 P-10ES Sect-8.2 P-11ES Sect-8.2 P-12ES Sect-8.2 P-13ES Sect-8.2 P-14ES Sect-8.2 P-15ES Sect-8.2 P-16ES Sect-8.2 P-17ES Sect-8.2 P-18ES Sect-8.2 P-19ES Sect-8.2 P-20ES Sect-8.2 P-21ES Sect-8.2 P-22ES Sect-8.2 P-23ES Sect-8.2 P-24ES Sect-8.2 P-25ES Sect-8.2 P-26ES Sect-8.2 P-27ES Sect-8.2 P-28ES Sect-8.2 P-29ES Sect-8.2 P-30ES Sect-8.2 P-31ES Sect-8.2 P-32ES Sect-8.2 P-33ES Sect-8.2 P-34ES Sect-8.2 P-35ES Sect-8.2 P-36ES Sect-8.2 P-37ES Sect-8.2 P-38ES Sect-8.2 P-39ES Sect-8.2 P-40ES Sect-8.2 P-41ES Sect-8.2 P-42ES Sect-8.2 P-43ES Sect-8.2 P-44ES Sect-8.2 P-45ES Sect-8.2 P-46ES Sect-8.2 P-47ES Sect-8.2 P-48ES Sect-8.2 P-49ES Sect-8.2 P-50ES Sect-8.2 P-51ES Sect-8.2 P-52ES Sect-8.2 P-53ES Sect-8.2 P-54ES Sect-8.2 P-55ES Sect-8.2 P-56ES Sect-8.3 P-1TY Sect-8.3 P-2TY Sect-8.3 P-3TY Sect-8.3 P-4TY Sect-8.3 P-5TY Sect-8.3 P-6TY Sect-8.3 P-1ES Sect-8.3 P-2ES Sect-8.3 P-3ES Sect-8.3 P-4ES Sect-8.3 P-5ES Sect-8.3 P-6ES Sect-8.3 P-7ES Sect-8.3 P-8ES Sect-8.3 P-9ES Sect-8.3 P-10ES Sect-8.3 P-11ES Sect-8.3 P-12ES Sect-8.3 P-13ES Sect-8.3 P-14ES Sect-8.3 P-15ES Sect-8.3 P-16ES Sect-8.3 P-17ES Sect-8.3 P-18ES Sect-8.3 P-19ES Sect-8.3 P-20ES Sect-8.3 P-21ES Sect-8.3 P-22ES Sect-8.3 P-23ES Sect-8.3 P-24ES Sect-8.3 P-25ES Sect-8.3 P-26ES Sect-8.3 P-27ES Sect-8.3 P-28ES Sect-8.3 P-29ES Sect-8.3 P-30ES Sect-8.3 P-31ES Sect-8.3 P-32ES Sect-8.3 P-33ES Sect-8.3 P-34ES Sect-8.3 P-35ES Sect-8.3 P-36ES Sect-8.3 P-37ES Sect-8.3 P-38ES Sect-8.3 P-39ES Sect-8.3 P-40ES Sect-8.3 P-41ES Sect-8.3 P-42ES Sect-8.3 P-43ES Sect-8.3 P-44ES Sect-8.3 P-45ES Sect-8.3 P-46ES Sect-8.3 P-47ES Sect-8.4 P-1TY Sect-8.4 P-2TY Sect-8.4 P-3TY Sect-8.4 P-4TY Sect-8.4 P-5TY Sect-8.4 P-6TY Sect-8.4 P-7TY Sect-8.4 P-8TY Sect-8.4 P-9TY Sect-8.4 P-10TY Sect-8.4 P-1ES Sect-8.4 P-2ES Sect-8.4 P-3ES Sect-8.4 P-4ES Sect-8.4 P-5ES Sect-8.4 P-6ES Sect-8.4 P-7ES Sect-8.4 P-8ES Sect-8.4 P-9ES Sect-8.4 P-10ES Sect-8.4 P-11ES Sect-8.4 P-12ES Sect-8.4 P-13ES Sect-8.4 P-14ES Sect-8.4 P-15ES Sect-8.4 P-16ES Sect-8.4 P-17ES Sect-8.4 P-18ES Sect-8.4 P-19ES Sect-8.4 P-20ES Sect-8.4 P-21ES Sect-8.4 P-22ES Sect-8.4 P-23ES Sect-8.4 P-24ES Sect-8.4 P-25ES Sect-8.4 P-26ES Sect-8.4 P-27ES Sect-8.4 P-28ES Sect-8.4 P-29ES Sect-8.4 P-30ES Sect-8.4 P-31ES Sect-8.4 P-32ES Sect-8.4 P-33ES Sect-8.4 P-34ES Sect-8.4 P-35ES Sect-8.4 P-36ES Sect-8.4 P-37ES Sect-8.4 P-38ES Sect-8.4 P-39ES Sect-8.4 P-40ES Sect-8.4 P-41ES Sect-8.4 P-42ES Sect-8.4 P-43ES Sect-8.5 P-1TY Sect-8.5 P-2TY Sect-8.5 P-3TY Sect-8.5 P-4TY Sect-8.5 P-5TY Sect-8.5 P-6TY Sect-8.5 P-7TY Sect-8.5 P-8TY Sect-8.5 P-9TY Sect-8.5 P-10TY Sect-8.5 P-1ES Sect-8.5 P-2ES Sect-8.5 P-3ES Sect-8.5 P-4ES Sect-8.5 P-5ES Sect-8.5 P-6ES Sect-8.5 P-7ES Sect-8.5 P-8ES Sect-8.5 P-9ES Sect-8.5 P-10ES Sect-8.5 P-11ES Sect-8.5 P-12ES Sect-8.5 P-13ES Sect-8.5 P-14ES Sect-8.5 P-15ES Sect-8.5 P-16ES Sect-8.5 P-17ES Sect-8.5 P-18ES Sect-8.5 P-19ES Sect-8.5 P-20ES Sect-8.5 P-21ES Sect-8.5 P-22ES Sect-8.5 P-23ES Sect-8.5 P-24ES Sect-8.5 P-25ES Sect-8.5 P-26ES Sect-8.5 P-27ES Sect-8.5 P-28ES Sect-8.5 P-29ES Sect-8.5 P-30ES Sect-8.5 P-31ES Sect-8.5 P-32ES Sect-8.5 P-33ES Sect-8.5 P-34ES Sect-8.5 P-35ES Sect-8.5 P-36ES Sect-8.5 P-37ES Sect-8.5 P-38ES Sect-8.5 P-39ES Sect-8.5 P-40ES Sect-8.5 P-41ES Sect-8.5 P-42ES Sect-8.5 P-43ES Sect-8.5 P-44ES Sect-8.5 P-45ES Sect-8.5 P-46ES Sect-8.5 P-47ES Sect-8.5 P-48ES Sect-8.5 P-49ES Sect-8.5 P-50ES Sect-8.5 P-51ES

Math
Discrete Mathematics With Applications 5th Edition

Discrete Mathematics With Applicat...

Solutions

Discrete Mathematics With Applicat...

In each of 7-14, relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R. A = { − 5 , − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4 , 5 } R is defined on A as follows: For all m , n ∈ Z .

m R n ⇔ 3 ( m 2 − n 2 ) .

Still sussing out bartleby?

The Solution to Your Study Problems

Chapter 8 Solutions

MathDiscrete Mathematics With Applications5th Edition

Discrete Mathematics With Applicat...

Solutions

Discrete Mathematics With Applicat...

In each of 7-14, relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R. A = { − 5 , − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4 , 5 } R is defined on A as follows: For all m , n ∈ Z . m R n ⇔ 3 ( m 2 − n 2 ) .

Still sussing out bartleby?

The Solution to Your Study Problems

Chapter 8 Solutions

Math
Discrete Mathematics With Applications 5th Edition

In each of 7-14, relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R. A = { − 5 , − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4 , 5 } R is defined on A as follows: For all m , n ∈ Z .

m R n ⇔ 3 ( m 2 − n 2 ) .