Exercise 5: A. Represent each of these relations on {1, 2, 3} with a matrix (with the elements of this set listed in increasing order). B. Draw the digraphs representing each of the relations below. C. Determine whether the relations represented by the directed graphs in part B are reflexive, symmetric, antisymmetric, asymmetric, irreflexive and/or transitive. a) {(1, 1), (1, 2), (1, 3)} А. C

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.7: Applications
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Exercise 5:
A. Represent each of these relations on {1, 2, 3} with a matrix (with the elements of this set
listed in increasing order).
B. Draw the digraphs representing each of the relations below.
C. Determine whether the relations represented by the directed graphs in part B are reflexive,
symmetric, antisymmetric, asymmetric, irreflexive and/or transitive.
а) {(1, 1), (1, 2), (1, 3)}
А.
B
C
b) {(1, 2), (2, 1), (2, 2), (3, 3)}
А.
C
Transcribed Image Text:Exercise 5: A. Represent each of these relations on {1, 2, 3} with a matrix (with the elements of this set listed in increasing order). B. Draw the digraphs representing each of the relations below. C. Determine whether the relations represented by the directed graphs in part B are reflexive, symmetric, antisymmetric, asymmetric, irreflexive and/or transitive. а) {(1, 1), (1, 2), (1, 3)} А. B C b) {(1, 2), (2, 1), (2, 2), (3, 3)} А. C
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