**Question 6** A relation \( R \) on a set \( X \) is called a **total order** if it is antisymmetric, reflexive, transitive, and if all elements of \( X \) are comparable (that is, for every pair \( x_1, x_2 \in X \) either \( x_1 R x_2 \) or \( x_2 R x_1 \)).**(a)** Construct a total order on the set \( X = \{\alpha, B, \oplus, 13\} \).**(b)** How many possible total orders are there on a finite set of cardinality \( n \)?

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Answered: 6. A relation R on a set X is called a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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6. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation xRy when x + y is divisible by 3, then R = O {1, 2), (2, 4)} all of these O {(1, 2), (2, 4), (3, 3)} O {1, 2), (3, 3)}
You just bought a new car from a dealership that sells cars no older than 2015. Consider therelationship to be the “same age.” The relation is “same age” and the set is cars made in 2015, 2016,2017, 2018, 2019, and 2020. (a) Prove that this relation is an equivalence relation. (b) Describe the partition defined by the equivalence classes
Let ? = {1, 2, 3, 4, 5, 6, 7} and define a relation ? ⊆ ? × ? by? = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6), (5,5)}Determine (yes or no) whether ? has the following properties (no justification is required).
Provide right answer with complete solution Answer letter C only.
A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain of a relation R where 2 cars are related if they were made in the same year. b) Describe the partition defined by the equivalence classes. How do I do this?
Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the following are true: ● • (5,0) = R; (8, 6) # R; |[1] R = 2. ●
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
What is the possible number of reflexive relations on a set of 5 elements?
prove why each relation has or does not have theproperties: reflexive, symmetric, anti-symmetric, transitive. 1) Let A = { set of all people }, relation R: A x A where R = { (a,b) | a,b ∈ A, a is at least as tall as b }
DISCRETE MATHEMATICS
prove why each relation has or does not have theproperties: reflexive, symmetric, anti-symmetric, transitive. 4) Z+ is the set of positive integers, relation R: Z+x Z+, a,b,c,d ∈ Z+; (a,b),(c,d) ∈ R if an only if a + d = b + c.

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