Which relations are partial order? more than one answer Let A={1,5,6,8,10}and R={(1,1), (5,5), (8,8), (10,10), (1,5), (5,6), (1,6),(6,8)} Let A={1,5,6,8,10}and R={(1,1), (5,5), (8,8), (10,10), (1,5), (5,6), (1,6), (6,6)} A={5,6,8,10,20} and R={ (a,b) ∈ A × A ; a divides b} None of the propsed relations

Answered: Image /qna-images/answer/54799640-3d96-44c6-bf8f-6e6a2125b609.jpg

Answered: Let A={1,5,6,8,10} and R={(1,1),…

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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1
What is the composite of the relations R and S, where R is the relation from {1, 2, 3} to {1, 2, 3, 4} with R = {(1, 1), (1, 4), (2, 3), (3, 1), (3, 4)} and S is the relation from {1, 2, 3, 4} to {0, 1, 2} with S = {(1, 0), (2, 0), (3, 1), (3, 2), (4, 1)}?
choose all the correct ones:
If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, what is the reflexive closure of R? O {(1, 2), (2, 1). (1, 4), (4, 1). (2, 3), (3, 2), (3, 1). (1, 3), (4, 2), (2, 4)} O {(1, 1), (1, 2), (1, 4), (2, 2), (2, 3), (3, 1), (3, 3), (4, 2), (4, 4)} O {(1, 2), (1, 4), (2, 3). (3, 1), (4, 2)} O {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1). (3. 2). (3, 3), (3, 4), (4, 1), (4, 2). (4, 3), (4, 4)}
1
Let A be a set and define A = {1,2, x,y}. So which of the following is A2 ?
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).
2. Let A = {1,2, 3}, B = {4, 5, 6}, C = {7,8, 9}. Consider the relations R from A to B, S from B to C, and T on A. R = {(1, 5), (2, 4), (1, 6)} S = {(4, 8), (5, 7), (6, 8), (6, 9)} Т 3 {(1,2), (2, 3), (3, 1), (1, 1), (2, 2), (3, 3)} Find the following relations (a) Find the compositions Ro S, T o R, T o T. (b) Find the matrices MR, Ms, MT, MTOT, MTOR and MRos of the respective relations R, S, т, То Т, То R, and Ro S.
A={1,2,3,4} & R={(1,1),(1,2),(2,1),(2,2,),(3,4),(4,3),(3,3),(4,4)} Determine Equivalence classes, Rank of R ; A/R.
Which of the following relations is the a partial ordering on the set A = {3,7,9}? {(3,3),(7,7), (3,9),(9,7), (9,9)} O {(3,3),(7,7),(7,9),(9,9), (9,7)} O 3,3,7,7,9,9,3,7,7,9,3,9 O None of the others O {(3,3),(3,7),(7,9),(7,7),(9,9)}
Explain whny the following binary relation on. 1,2,3} Is not R= {(1,1)(1,2),(1,3),(2,1).(2,2).(3,3)}|

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		Let A={1,5,6,8,10} and R={(1,1), (5,5), (8,8), (10,10), (1,5), (5,6), (1,6),(6,8)}
		Let A={1,5,6,8,10} and R={(1,1), (5,5), (8,8), (10,10), (1,5), (5,6), (1,6), (6,6)}
		A={5,6,8,10,20} and R={ (a,b) ∈ A × A ; a divides b}
		None of the propsed relations

Let A={1,5,6,8,10} and R={(1,1), (5,5), (8,8), (10,10),