6. A relation R on a set X is called a total order if it is antisymmetric, reflexive, transi-tive, and if all elements of X are comparable (that is, for every pair x₁, x2 € X eitherx₁ Rx₂ or x₂ Rx₁).(a) Construct a total order on the set X={a, B, Ⓒ, 13}.(b) How many possible total orders are there on a finite set of cardinality n?

Answered: Image /qna-images/answer/2befd691-8083-4ab6-ba40-4099aa0c9d2c.jpg

6. A relation R on a set X is called a total order if it is antisymmetric, reflexive, transi- tive, and if all elements of X are comparable (that is, for every pair x₁, x2 € X either x₁ Rx2 or x2 Rx1). (a) Construct a total order on the set X = {a, B, Ⓒ, 13}. (b) How many possible total orders are there on a finite set of cardinality n?

6. A relation R on a set X is called a total order if it is antisymmetric, reflexive, transi- tive, and if all elements of X are comparable (that is, for every pair x₁, x2 € X either x₁ Rx2 or x2 Rx1). (a) Construct a total order on the set X = {a, B, Ⓒ, 13}. (b) How many possible total orders are there on a finite set of cardinality n?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 17E: Does the relation is a brother of have a reflexive property consider one male? A symmetric property...

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