(24 pts) Either show the following relations are equivalence relations, or show whichqualities of an equivalence relation they lack:a. S = {0,1,2,3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)}b. S is the set of all dog owners. R = {(a, b): a and b own the same breed of dog}

a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Answered: (24 pts) Either show the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

. Let R1, R2, R3 be relations on { a, b, c, d, e }. Find the transitive closures, given their definitions below. i) R1 = { (a, c),(b, d),(c, a),(d, b),(e, d) } ii) R2 = { (b, c),(b, e),(c, e),(d, a),(e, b),(e, c) } iii) R3 = { (a, b),(a, c),(a, e),(b, a),(b, c),(c, a), (c, b),(d, a),(e, d) }
7. List the coordinate pairs needed in order to turn the following relations into equivalence relations. AR
This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations R and S from a set A to a set B, RUS = {(x, y) E AXB I (x, y) ER or (x, y) E S} RNS = {(x, y)E AXB| (x, y) ER and (x, y) Es}. Let A = {-2, 2, 3, 5} and B = {2, 3} and define relations R and S from A to B as follows: For every (x, y) E Ax B, x R y - |x| = lyl and xsyex - y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, RU S, and RN s. (Enter your answers as comma-separated lists of ordered pairs.) AXB = R = S = RUS = ROS =
Let R be an equivalence relation on A = {0, 7, 8, 9} and R = {(7, 8), (8,9), (9, 9), (7, 7), (8, 8), (7, 9), (9, 7), (9, 8), (8, 7), (0, 0)}. Answer each of the following questions. [8] = [7] = [9] = [0] =
1. Let A = {1,2,3,4,5,6), and consider the following equivalence relation on A: R = {(1, 1), (2, 2), (3, 3), (4,4), (5,5), (6, 6), (2, 3), (3, 2), (4, 5), (5, 4), (4, 6), (6,4), (5,6), (6,5)} List the equivalence classes of R. 2. Let A = {a,bed el Suppose A is an equivalence relation on 4. Suppose R bes two equivaler.se alasses. Also wad, Re and aRd Write out R as a cot 3. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has three equivalence classes. Also aRd and bRc. Write out R as a set. 4. Let A {a,b,c,d,e). Suppose A is an equivalence relation on 4. Suppose also that anta and one, aRa and cite. How many equivalones classes dees At have! CIV 5. There are two different equivalence relations on the set A = {a,b}. Describe them. Diagrams will suffice.
15 Part 2 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) = R² | a> b), the greater than relation R₂ = {(a, b) ER² | a2 b), the greater than or equal to relation R3 = {(a, b) ER² | a< b), the less than relation R₁ = {(a, b) ER² | a ≤ b), the less than or equal to relation R₁ = {(a, b) = R² | a = b), the equal to relation R6 = {(a, b) ER² | a b), the unequal to relation For these relations on the set of real numbers, find R₁⁰ R₁. Multiple Choice O O R₁ O R4
17 Part 4 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) € R² | a> b), the greater than relation R₂ = {(a, b) ER² | a2 b), the greater than or equal to relation R3 = {(a, b) ER² | a< b), the less than relation R₁ = {(a, b) ER² | a ≤ b), the less than or equal to relation R₁ = {(a, b) = R² | a = b), the equal to relation R₁ = {(a, b) € R² | a‡ b), the unequal to relation For these relations on the set of real numbers, find R₁ R6. Multiple Choice O O о R5 R² R6
2. Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on A and find the quotient set A. (a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁. (b) (a,b) = (a₁, b₁) if ab = a₁b₁. (c) (a, b) = (a₁, b₁) if a = a₁. (d) (a, b) = (a₁, b₁) if a - b = a₁-b₁.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

(24 pts) Either show the following relations are equivalence relations, or show which qualities of an equivalence relation they lack: a. S = {0,1,2,3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} b. S is the set of all dog owners. R = {(a, b): a and b own the same breed of dog}