Explanation Given information: The relation R is an equivalence relation on the set A. A = { 1 , 2 , 3 , 4 , ... , 20 } . R is defined on A as follows: For all x , y ∈ A , x R y ⇔ 4 | ( x − y ) . Calculation: A = { 1 , 2 , 3 , 4 , … , 20 } R = { ( x , y ) ∈ A × A | 4 ( x − y ) } Let us first group the ordered pairs in R that have at least one common element (with at least one of the other elements in the group). 4 | ( x − y ) is true if and only if x − y is a multiple of 4 if and only if x and y differ by 0, 4, 8, 12 or 16 (as the elements are between 1 and 20). Thus ( x − y ) ∈ R when x and y differ by 0, 4, 8, 12 or 16. First group: ( 1 , 1 ) , ( 1 , 5 ) , ( 1 , 9 ) , ( 1 , 13 ) , ( 1 , 17 ) ( 5 , 1 ) , ( 5 , 5 ) , ( 5 , 9 ) , ( 5 , 13 ) , ( 5 , 17 ) ( 9 , 1 ) , ( 9 , 5 ) , ( 9 , 9 ) , ( 9 , 13 ) , ( 9 , 17 ) ( 13 , 1 ) , ( 13 , 5 ) , ( 13 , 9 ) , ( 13 , 13 ) , ( 13 , 17 ) ( 17 , 1 ) , ( 17 , 5 ) , ( 17 , 9 ) , ( 17 , 13 ) , ( 17 , 17 ) Second group: ( 2 , 2 ) , ( 2 , 6 ) , ( 2 , 10 ) , ( 2 , 14 ) , ( 2 , 18 ) ( 6 , 2 ) , ( 6 , 6 ) , ( 6 , 10 ) , ( 6 , 14 ) , ( 6 , 18 ) ( 10 , 2 ) , ( 10 , 6 ) , ( 10 , 10 ) , ( 10 , 14 ) , ( 10 , 18 ) ( 14 , 2 ) , ( 14 , 6 ) , ( 14 , 10 ) , ( 14 , 14 ) , ( 14 , 18 ) ( 18 , 2 ) , ( 18 , 6 ) (

5th Edition

ISBN: 9780357540244

Author: EPP

Publisher: CENGAGE L

See similar textbooks

Videos

Question

Chapter 8.3, Problem 5ES

To determine

To find the distinct equivalence classes of R.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 4ES

Chapter 8.3, Problem 6ES

Students have asked these similar questions

Find a second-order homogeneous linear ODE for which 1, e3x are solutions

Section 2.2 Subsets 71 Exercise Set 2.2 Practice Exercises In Exercises 1-18, write or in each blank so that the resulting statement is true. 1. {1, 2, 5} {1, 2, 3, 4, 5, 6, 7} 2. {2, 3, 7} {1, 2, 3, 4, 5, 6, 7} 3. {-3, 0, 3} {-4,-3,-1, 1, 3, 4} 4. {-4, 0, 4} 5. {Monday, Friday} {-3, -1, 1, 3} {Saturday, Sunday, Monday, Tuesday, Wednesday} 6. {Mercury, Venus, Earth} {Venus, Earth, Mars, Jupiter} 7. {x/x is a cat} {xx is a black cat} {x|x is a pure-bred dog} ibrary mbers, ause the entire sual 8. {xx is a dog} 9. (c, o, n, v, e, r, s, a, t, i, o, n} {v, o, i, c, e, s, r, a, n, t, o, n} 10. [r, e, v, o, l, u, t, i, o, n} {t, o, l, o, v, e, r, u, i, n} 33. A = {x|x E N and 5 < x < 12} B = {x|x E N and 2 ≤ x ≤ 11} A_ B 34. A = {x|x = N and 3 < x < 10} B = A. {x|x = N and 2 ≤ x ≤ 8} B 35. Ø {7, 8, 9,..., 100} 36. Ø _{101, 102, 103, . . ., 200} 37. [7, 8, 9,...} 38. [101, 102, 103, ...} 39. Ø 40. { } { } e In Exercises 41-54, determine whether each statement is true or false. If…

A truck loaded with rocks weighs 14,260 lb. If the truck weighs 8420 lb, how much do the rocks weigh?

Chapter 8 Solutions

WEBASSIGN F/EPPS DISCRETE MATHEMATICS

Ch. 8.1 - If R is a relation from A to B, xA , and yB , the...Ch. 8.1 - Prob. 2TY Ch. 8.1 - Prob. 3TY Ch. 8.1 - Prob. 4TY Ch. 8.1 - If R is a relation on a set A, the directed graph...Ch. 8.1 - As in Example 8.1.2, the congruence modulo 2...Ch. 8.1 - Prove that for all integers m and n,m-n is even...Ch. 8.1 - The congruence modulo 3 relation, T, is defined...Ch. 8.1 - Define a relation P on Z as follows: For every...Ch. 8.1 - Prob. 5ES

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To find the distinct equivalence classes of R.

Solution Summary: The author explains that R is an equivalence relation on the set A. They first group the ordered pairs in R that have at least one common element.

Videos

To find the distinct equivalence classes of R.

Want to see the full answer?

Chapter 8 Solutions