1. Consider the relation R = {(a, a),(b, b), (c, c), (d, d),(a, b), (b,a)} on set A = {a,b,c,d}.Is R reflexive? Symmetric? Transitive? If a property does not hold, say why.2. Consider the relation R = {(a,b),(a, c), (c, c), (b, b), (c, b), (b,c)} on the set A = {a,b,c}.Is R reflexive? Symmetric? Transitive? If a property does not hold, say why.3. Consider the relation R = {(a, b),(a, c), (c, b), (b, c)} on the set A = {a,b,c}. Is Rreflexive? Symmetric? Transitive? If a property does not hold, say why.

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Answered: 1. Consider the relation R = {(a,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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3. Let S = R × R and R be the relation on S defined by (a, b)R(c, d) iff a+c=b+d. Determine whether R is reflexive, symmetric, and/or transitive. %3D
Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, 3),(2, 4),(4, 1),(2, 1),(1, 2),(3, 2)} (a) Is R symmetric? Justify your answer. (b) Is R transitive?
Let A = {a, b, c, d, and let R be the relation R = {(a, a), (b, b), (c, c), (d, d), (c, b), (a, d), (b, a), (b, d), (c, d), (c, a)}. Is R a total order on A? Yes No Justify your answer. (Select all that apply.) R is antisymmetric. R is not antisymmetric. There exists a chain in R that contains every element of A. There does not exist a chain in R that contains every element of A. R is transitive. R is not transitive. Each element of A exists in R. Each element of A does not exist in R. R is reflexive. R is not reflexive.
Let R be the relation on a set A = {a, b, c, d} defined by R = {(a, a), (a, b), (b, b), (b, c), (c, b), (d, c)}. Find R² and R³.
Let A = (0,1,2,3). The relations R, S and T in the set A are defined as follows…R={(0,0),(0,1),(0,3),(1,0),(1,1),(1,3),(2,2),(3,0),(3,1),(3,3)}S ={(0,0),(0,2),(0,3),(2,3)}T={(0,1),(2,3)}Find the equivalent relation is:
Discrete math: please provide me 100% accurate answers
. 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) }
Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive
Let X=\{a,b,c,d,e,f\}X={a,b,c,d,e,f} and SS be the relation on XX defined by S = \{ (a,a), (a,b), (a,c),S={(a,a),(a,b),(a,c), (a,d), (a,e), (a,f),(a,d),(a,e),(a,f), (b,b), (b,d), (b,e),(b,b),(b,d),(b,e), (b,f), (c,c), (c,d),(b,f),(c,c),(c,d), (c,e), (c,f), (d,d),(c,e),(c,f),(d,d), (d,e), (d,f), (e,e), (f,f) \}(d,e),(d,f),(e,e),(f,f)}. Is SS a partial order? If so, draw its Hasse diagram. If not, give an example showing why.

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1. Consider the relation R = {(a, a),(b, b), (c, c), (d, d),(a, b), (b, a)} on set A = {a,b,c,d}. Is R reflexive? Symmetric? Transitive? If a property does not hold, say why.