(a) Give an example of a relation on the set {a, b, c, d} which is symmetric andtransitive, but not reflexive.(b) Let R be the equivalence relation on the set S = {1, 3, 5, 7,..., 49} defined byxRy if and only if x = y (mod 10).Give the equivalence classes for the relation R on S.Justify your answers!

(a) Given set is: a, b, c, d. To Do: We have to give an example of a relation on the given set a, b,…

Answered: (a) Give an example of a relation on…

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

3. Let R be a relation defined on the set A = N × N where (a, b) R (c, d) if að = cd. Show R is an equivalence relation. Then, list the elements of the equivalence class [(9, 2)].
Prove or disprove the following statements
5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence relation? Prove or disprove. b) Is this relation antisymmetric? Prove or disprove.
Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common biological parent} Show whether or not R is an equivalence relation.
5) What is the cardinality of the set {characters in set A}? 6) Let X = {strings in A}. Find |X 7) Let X {strings in A} Name two B, CC X and two D, ECX such that... a) BUC X B = C = b) DNE #Ø E = 8) Suppose we define a relation on the set {strings in A} by making 69°F a
Let - be a relation on N defined as: a ~b if a < (b – 1). (i) Is ~ reflexive? Prove your answer. (ii) Is ~ (iii) Is ~ transitive? Prove your answer. symmetric? Prove your answer.
Let R be the relation on the set of all people who have visited a particular Web page such that x Ry if and only if person x and person y have followed the same set of links starting at this Web page (going from Web page to Web page until they stop using theWeb). Show that R is an equivalence relation.
Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x + 2y). If S = {−7, −6, −2, 0, 1, 4, 5, 7}, then what are the distinct equivalence classes in this case? Please show how you find them
Let S be a nonempty set. Consider the relation ~ on P(S) defined by A ~ B if AUBC = S. Is the relation an equivalence relation? Explain. If yes, identify (no need to justify) the equivalence class of
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
Let R be the relation on the set of all mathematicians that contains the ordered pair (a, b) if and only if a and b have written a published mathematical paper together. a) Describe the relation R[2] in the context of the problem.b) Describe the relation R* in the context of the problem.c) The Erdos number of a mathematician is 1 if this mathematician wrote a paper with the prolific Hungarian mathematician Paul Erdos. The Erdos number is 2 if a mathematician didn’t write a joint paper with Erdos but wrote a joint paper with someone who wrote a joint paper with Erdos, and so on (except that the Erdos number of Erdos himself is 0). Give a definition of the Erdos number is terms of paths in R. List a name of a mathematician with number: 1, 2, and 3
Let R be an equivalence relation on A = {0, 1,5, 6, 8, 9} and R = {(6, 1), (1,6), (6, 6), (1, 1), (0, 0), (5, 5), (5, 8), (5,9), (8,5), (8, 8), (8, 9), (9, 5), (9, 8), (9,9)}. Show the partition of A defined by the equivalence classes of R.

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

(a) Give an example of a relation on the set {a, b, c, d] which is symmetric and transitive, but not reflexive. (b) Let R be the equivalence relation on the set S = {1, 3, 5, 7,..., 49} defined by *Ry if and only if x = y (mod 10). Give the equivalence classes for the relation R on S.