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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
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) \( R_1 \oplus R_2 \).
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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