Let R1 and R2 be relations on a set A represented by the matrices 0 1 07 1 1 1 1 0 0 0 1 = |0 1 1 MRI and MR:
Let R1 and R2 be relations on a set A represented by the matrices 0 1 07 1 1 1 1 0 0 0 1 = |0 1 1 MRI and MR:
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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![Let \( R_1 \) and \( R_2 \) be relations on a set \( A \) represented by the matrices
\[
M_{R_1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 0 \end{bmatrix}
\]
and
\[
M_{R_2} = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}.
\]
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) \( R_1 \oplus R_2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb89e603e-61c2-4a4b-a30b-7e019f65a9c9%2F078c2015-10be-4e45-9a7e-872469446857%2Fqnqpsua_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
\[
M_{R_1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 0 \end{bmatrix}
\]
and
\[
M_{R_2} = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}.
\]
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) \( R_1 \oplus R_2 \).
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