Problem 26. Consider the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6):Find the partition generated by RR= {(1, 1), (2, 2), (3, 3), (4,4), (5,5), (6, 6), (1, 2), (1,4), (2, 1), (2, 4), (4, 1), (4, 2), (3,6), (6,3)}.

Answered: Image /qna-images/answer/8e20311a-bed2-4ce4-be4c-d126cd65db53.jpg

Answered: Problem 26. Consider the following…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 16E

See similar textbooks

Similar questions

Consider the relations R = {(1,5), (2, 2), (3, 4), (5, 2)}, S = {(2,4), (3, 4), (3, 1), (5, 5)}, T = {(1,4), (3, 5), (4, 1)} on the set A = {1,2,3, 4, 5}. Find (a) SoR = (b) RoT = (c) ToS = (d) Ro R= (e) SoS = (() ТоТ%—
2. Let A = {1,2, 3, 4}, B = {a, ß, 7}, C = {x, y, z}. Consider the relations R from A to B and S from B to C as follows: R = {(1,8), (3, a), (3, 3), (4, 7)} and S = = {(a, y), (7, x), (a, z)} Find the following relations (a) Draw the diagrams of R and S. (b) Determine Ro S. (c) Find the matrix of each relation R, S and Ro S (d) Write R-1 and Ro S as sets of ordered pairs.
Given the relation R- {(1,1), (2.2), (3,3),(4.4), (1.,2). (2.1). (3,4), (4,3))} on the set X= (1,2.3.4). select the set corresponding to (3). (3) (4) (3,4) This is not an equivalence relation and therefore does not have equivalence classes.
3. Let A = {1,2,3,4,5,6}. Given the equivalence relation R = {(1,1), (2,2), (3,3), (4,4), (5,5), (1,3), (3,1), (6,6), (2,4), (4,2), (4,5), (2,5), (5,4), (5,2)} on A. Find the equivalence class of each element of A. How many distinct equivalence classes are there on A.
3. Let A = {-1, –3, – 5}, B = {a, B, 7}, C = {x, y, z}. Consider the relations R from A to B and S from B to C respectively. R = {(-1,8), (–3, a), (–3, 7)} and S = {(a, y), (B, x), (7, y), (y, 2)} Find the following relations (a) Find the composition Ro S. (b) Find the matrices MR, Ms and MRos of the respective relations R, S and Ro S. (c) Compare M Ros to the product MRMS.
Question 6 Given the relation R= {(1,1), (2.2). (3,3),(4,4), (1,2), (2.1). (3,4) (4,3)} on the set X= {1,2.3,4), select the set corresponding to (3). {3} (4) (3,4) This is not an equivalence relation and therefore does not have equivalence classes.
2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is divisible by 4, then R = O {(2,2), (2,4)} O {(2,3)} O none of these O {(1,3), (2,4)}
5. Let A={4, 5,6} and B= {5,6,7} and define relations R,S, and T from A to B as follows: %3D For all (x, y) E Ax B, (x, y) e R means that x 2 y x-YEZ (x, y) eS means that T = {(4,5).(6,5).(6, 7)} Draw an arrow diagrams for R, S, and T. b. Indicate whether any of the relations R, S, and T are functions. Explain your answer. a.
VIII.1. Let A = {1,2, 3, 4} and let R, S, T and U be the following relations: R= {(1,3), (3, 2), (2, 1), (4, 4)}, S = {(2,1), (3, 3), (4, 2)}, T = {(4,1), (4, 2), (3, 1), (3, 2), (1, 2)}, U = {(x, y) | x > y}. (a) For each of R, S, T and U determine whether they are functional, reflexive, symmetric, anti-symmetric or transitive. Explain your answer in each case, showing why your answer is correct. (b) What is the transitive closure of R? (c) Explain why R", the transitive closure of R, is an equivalence relation. De- scribe the equivalence classes E, into which the relation partitions the set A. VIII.2. Prove or give a counterexample to the following statement: for any relation R both R and RoR always have the same transitive closure. VIII.3. Is there a mistake in the following proof that any transitive and symmetric relation Ris reflexive? If so, what is it? Let a Rb. By symmetry, bRa. By transitivity, if aRb and bRa, then aRa. This proves reflexivity. VIII.4. Determine for the…
5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1, 3), (2, 3), (2, 4), (3, 1), (3, 4), (3, 5), (4, 2), (4, 5), (5, 1), (5,2), and (5, 4). Find, a) R² b) R³ c) R4 d) R5
3. Given the relation R1 from X = {1,2,3,4} to Y = {a,b,c} and R2 from Y = {a,b,c} and Z = {6,7,8} where R1 = {(1,a).(2,a). (2,b),(3,c),(4.a)} and R2 = {(a,6), (a,7), (a,8), (b.7), (b,8), (c.6), (c.8)} Use matrices to find the value R2 · R1.
9. List the ordered pairs in the equivalence relation on A = {1, 2, 3, 4, 5} associated with these partitions: (a) {{1,2},{3, 4, 5}} (c) {{2, 3, 4, 5}, {1}} ★ (b) (d) {{1}, {2}, {3,4}, {5}} {{1,5}, {2,4}, {3}}

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

SEE MORE TEXTBOOKS

Problem 26. Consider the following equivalence relation on the set A = {1, 2, 3, 4, 5, 6): Find the partition generated by R R= {(1, 1), (2, 2), (3, 3), (4,4), (5,5), (6, 6), (1, 2), (1,4), (2, 1), (2, 4), (4, 1), (4,2), (3,6), (6,3)}.