This is set theory Question 5. Let ~ be the equivalence relation defined on Z byx~ Y3 divides (xy)For each x Z, let [x] be the ~-equivalence class which contains x; and let Z/~be the set of ~-equivalence classes.12361 PRACTICE FIRST MIDTERM QUESTIONS 2024(i) Prove that the multiplication operation on Z/ ~ given byx-y=xyis well-defined.(ii) Determine whether the exponentiation operation on Z/ ~ given by[x][v] = [x]is well-defined.

(i) Proving that the multiplication operation on Z/∼ given by [x][y] = [xy] is well-defined:…

Answered: Question 5. Let ~ be the equivalence…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...

See similar textbooks

Similar questions

a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the equivalence class [ 3 ]. b. Let R be the equivalence relation congruence modulo 4 that is defined on Z in Example 4. For this R, list five members of equivalence class [ 7 ].
Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
The relation R on the set of all integer numbers is defined by (x, y) = R_if and only if |x| = [y]. Then, R is an equivalence relation. True False
The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1, 00). Can X1, X2, X3 be equivalence classes with respect to some equivalence relation on R? O No, they can't be equivalence classes for some equivalence relation since X1n X2 + 0. O No, they can't be equivalence classes for some equivalence relation since any equivalence relation on infinite set has infinitely many different equivalence classes. O Yes, these sets can be equivalence classes for some equivalence relation since X1 U X2 U X3 = R. O Yes, these sets can be equivalence classes for some equivalence relation since X2n X3 = 0.
Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b), how do you determine when to stop? please show the steps to get the equivalence classes in detail, thank you in advance.
2 Explain why the relation on N defined as is not an equivalence relation. {(x, y): x+y is a multiple of 3}
What is equivalence relation
Help please!
Give a binary relation R on an n-element set such that R != ∅ and |R ◦ R^(−1) | = n^(2) · |R^(−1) ◦ R|
(d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence classes.
Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; A2 = %3D {2,4, 6}; A3 = {3, 6}. Define the relation R on set A as follows: x R y if and only if { x, y} C A or { x, y}C A, or { x,y}C A. That is, x R y if and only if x and y are both in A, or x and y are both in A2 or x and y are both in A3.
We have defined the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R = (≡6)∩(≡10) is another subset of Z^2 , so it is also a relation on Z. The relation R is equal to ≡m for some natural number m. What is m?

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

SEE MORE TEXTBOOKS