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19. Let R= 1010 1100 0011 0100 be the adjacency matrix for a relation r on the set A = {1,2,3,4}. (a) Write down the complete set of ordered pairs for r. (b) Let s be the relation from A to B = {5,7,9} given by s = {(3,5), (3,7), (4,5)}. Compute the composition rs. (c) Compute R² using Boolean arithmetic. Then write down the elements of r². (d) State the definitions for an antisymmetric relation, symmetric relation, reflexive relation, and transitive relation. (e) Which of the properties from part (d) does r have? Use the definitions to justify your answer.

19. Let R= 1010 1100 0011 0100 be the adjacency matrix for a relation r on the set A = {1,2,3,4}. (a) Write down the complete set of ordered pairs for r. (b) Let s be the relation from A to B = {5,7,9} given by s = {(3,5), (3,7), (4,5)}. Compute the composition rs. (c) Compute R² using Boolean arithmetic. Then write down the elements of r². (d) State the definitions for an antisymmetric relation, symmetric relation, reflexive relation, and transitive relation. (e) Which of the properties from part (d) does r have? Use the definitions to justify your answer.

Advanced Engineering Mathematics
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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Pleasse this is a practice problem so I will be happy if you can explain it into details for me. I know how to solve part a) and part d). Please solve part b), d) and e). Thank you very much. 

19. Let R = 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 be the adjacency matrix for a relation r on the set A = {1,2,3,4}. (a) Write down the complete set of ordered pairs for r. (b) Let s be the relation from A to B = {5,7,9} given by s = {(3,5), (3, 7), (4,5)}. Compute the composition rs. (c) Compute R2 using Boolean arithmetic. Then write down the elements of r2. (d) State the definitions for an antisymmetric relation, symmetric relation, reflexive relation, and transitive relation. (e) Which of the properties from part (d) does r have? Use the definitions to justify your answer.
Transcribed Image Text:19. Let R = 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 be the adjacency matrix for a relation r on the set A = {1,2,3,4}. (a) Write down the complete set of ordered pairs for r. (b) Let s be the relation from A to B = {5,7,9} given by s = {(3,5), (3, 7), (4,5)}. Compute the composition rs. (c) Compute R2 using Boolean arithmetic. Then write down the elements of r2. (d) State the definitions for an antisymmetric relation, symmetric relation, reflexive relation, and transitive relation. (e) Which of the properties from part (d) does r have? Use the definitions to justify your answer.
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