Consider your eight-digit student ID as a set of single-digit integers. For example, if your student ID is the number 01238586, then it represents the set S = {0, 1, 2, 3, 5, 6, 8). Now consider your student ID as a sequence of eight digits. For example, if your student ID is the number 01238586, then it represents the sequence D= (0, 1, 2, 3, 8, 5, 8, 6). The sequence can be used to define a relation r:S→ S by creating the elements of r as follows, r = {(d₁, d₂), (dy, d4), (d5, de), (dr, de)} The di, 1 ≤ i ≤8 are the digits in the sequence read left to right. For example, if your student ID is the number 01238586, then r = {(0, 1), (2, 3), (8,5), (8,6)} Questions to Answer 1. Create the relation r using your student ID. Record the relation in roster notation as a set of 2-tuples (see example). 2. Extend your relation by adding the 2-tuple (d2, d₁) to r, creating the relation R. That is[R = r U {(d₂, d₁)}. Record the relation R as a set of 2-tuples. 3. Find the transitive closure, T, of the relation R. Record the relation T as a set of 2-tuples.
Consider your eight-digit student ID as a set of single-digit integers. For example, if your student ID is the number 01238586, then it represents the set S = {0, 1, 2, 3, 5, 6, 8). Now consider your student ID as a sequence of eight digits. For example, if your student ID is the number 01238586, then it represents the sequence D= (0, 1, 2, 3, 8, 5, 8, 6). The sequence can be used to define a relation r:S→ S by creating the elements of r as follows, r = {(d₁, d₂), (dy, d4), (d5, de), (dr, de)} The di, 1 ≤ i ≤8 are the digits in the sequence read left to right. For example, if your student ID is the number 01238586, then r = {(0, 1), (2, 3), (8,5), (8,6)} Questions to Answer 1. Create the relation r using your student ID. Record the relation in roster notation as a set of 2-tuples (see example). 2. Extend your relation by adding the 2-tuple (d2, d₁) to r, creating the relation R. That is[R = r U {(d₂, d₁)}. Record the relation R as a set of 2-tuples. 3. Find the transitive closure, T, of the relation R. Record the relation T as a set of 2-tuples.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Use S={0,2,3,4,6,9}
Use D=(2,0,4,6,9,4,3,4)
Transcribed Image Text:Consider your eight-digit student ID as a set of single-digit integers. For example, if your student ID is the number 01238586, then it represents the set
S= {0, 1, 2, 3, 5, 6, 8). Now consider your student ID as a sequence of eight digits. For example, if your student ID is the number 01238586, then it represents the
sequence D= (0, 1, 2, 3, 8, 5, 8, 6). The sequence can be used to define a relation r:S→ S by creating the elements of r as follows,
r = {(d₁, d₂), (dy, d₁), (d5, de), (dr, ds)}
The di, 1 ≤ i ≤8 are the digits in the sequence read left to right. For example, if your student ID is the number 01238586, then
r = {(0, 1), (2, 3), (8,5), (8,6)}
Questions to Answer
1. Create the relation r using your student ID. Record the relation in roster notation as a set of 2-tuples (see example).
2. Extend your relation by adding the 2-tuple (d2, d₁) to r, creating the relation R. That is[R = r U {(d2, d₁)}. Record the relation R as a set of 2-tuples.
3. Find the transitive closure, T, of the relation R. Record the relation T as a set of 2-tuples.
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