Let Rị and R2 be relations on a set A represented by the matrices [o i o° | 1 1 1 1 0 0 0 1 1 1 MRI and MR: a) R¡U R2. d) Rj 0 Rj. Find the matrices that represent b) RịN R2. e) R¡ Ð R2. c) R2o R1.
Let Rị and R2 be relations on a set A represented by the matrices [o i o° | 1 1 1 1 0 0 0 1 1 1 MRI and MR: a) R¡U R2. d) Rj 0 Rj. Find the matrices that represent b) RịN R2. e) R¡ Ð R2. c) R2o R1.
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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Question
just do d) and e)
![Let \( R_1 \) and \( R_2 \) be relations on a set \( A \) represented by the matrices
\[
M_{R_1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 0 \end{bmatrix} \quad \text{and} \quad M_{R_2} = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}.
\]
Find the matrices that represent:
a) \( R_1 \cup R_2 \).
b) \( R_1 \cap R_2 \).
c) \( R_2 \circ R_1 \).
d) \( R_1 \circ R_1 \).
e) \( R_1 \oplus R_2 \).
**Explanation of Terms:**
- \( R_1 \cup R_2 \) represents the union of the matrices. For each element, if it is 1 in either matrix, it will be 1 in the resulting matrix.
- \( R_1 \cap R_2 \) represents the intersection of the matrices. For each element, if it is 1 in both matrices, it will be 1 in the resulting matrix.
- \( R_2 \circ R_1 \) represents the composition of the relations. It involves matrix multiplication.
- \( R_1 \circ R_1 \) also represents the composition, where \( R_1 \) is composed with itself.
- \( R_1 \oplus R_2 \) represents the symmetric difference. For each element, it will be 1 if the matrices have differing values (i.e., 0 and 1 or 1 and 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb89e603e-61c2-4a4b-a30b-7e019f65a9c9%2F24dcdcb1-31e2-41df-acec-40b58cefcd1a%2Fvzry7be_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( R_1 \) and \( R_2 \) be relations on a set \( A \) represented by the matrices
\[
M_{R_1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 0 \end{bmatrix} \quad \text{and} \quad M_{R_2} = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}.
\]
Find the matrices that represent:
a) \( R_1 \cup R_2 \).
b) \( R_1 \cap R_2 \).
c) \( R_2 \circ R_1 \).
d) \( R_1 \circ R_1 \).
e) \( R_1 \oplus R_2 \).
**Explanation of Terms:**
- \( R_1 \cup R_2 \) represents the union of the matrices. For each element, if it is 1 in either matrix, it will be 1 in the resulting matrix.
- \( R_1 \cap R_2 \) represents the intersection of the matrices. For each element, if it is 1 in both matrices, it will be 1 in the resulting matrix.
- \( R_2 \circ R_1 \) represents the composition of the relations. It involves matrix multiplication.
- \( R_1 \circ R_1 \) also represents the composition, where \( R_1 \) is composed with itself.
- \( R_1 \oplus R_2 \) represents the symmetric difference. For each element, it will be 1 if the matrices have differing values (i.e., 0 and 1 or 1 and 0).
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