6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb if and only if a - b is a multiple of 3. (a) Represent the relation R as a subset of A × A (draw the corresponding table). (b) Show that R is reflexive, that is, for all a € A, we have a Ra. (c) Show that R is symmetric, that is, for all a, b = A, we have that a R b implies that b R a.
6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb if and only if a - b is a multiple of 3. (a) Represent the relation R as a subset of A × A (draw the corresponding table). (b) Show that R is reflexive, that is, for all a € A, we have a Ra. (c) Show that R is symmetric, that is, for all a, b = A, we have that a R b implies that b R 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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![**Relation on a Set: Problem 6**
Consider the set \( A = 10 = \{0, 1, 2, \ldots, 9\} \) and consider the relation \( R \) on \( A \) determined by
\[ a \, R \, b \quad \text{if and only if} \quad a - b \text{ is a multiple of 3}. \]
**Tasks:**
(a) Represent the relation \( R \) as a subset of \( A \times A \). (Draw the corresponding table).
(b) Show that \( R \) is reflexive, that is, for all \( a \in A \), we have \( a \, R \, a \).
(c) Show that \( R \) is symmetric, that is, for all \( a, b \in A \), we have that \( a \, R \, b \) implies that \( b \, R \, a \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf527488-7949-457b-8fb2-a06535c2214c%2F7c150ef3-ee25-40fa-a11d-56e7b00ef633%2Fc0svwcg_processed.png&w=3840&q=75)
Transcribed Image Text:**Relation on a Set: Problem 6**
Consider the set \( A = 10 = \{0, 1, 2, \ldots, 9\} \) and consider the relation \( R \) on \( A \) determined by
\[ a \, R \, b \quad \text{if and only if} \quad a - b \text{ is a multiple of 3}. \]
**Tasks:**
(a) Represent the relation \( R \) as a subset of \( A \times A \). (Draw the corresponding table).
(b) Show that \( R \) is reflexive, that is, for all \( a \in A \), we have \( a \, R \, a \).
(c) Show that \( R \) is symmetric, that is, for all \( a, b \in A \), we have that \( a \, R \, b \) implies that \( b \, R \, a \).
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