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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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Please do Exercise 17.1.13 part A,B,C,D and please show step by step and explain

**Exercise 17.1.13.** Let \( A = \{-2, -1, 0, 1, 2\} \). Draw a digraph for each of the following binary relations on \( A \): (a) \( R_a = \{ (x, y) \mid x^2 = y^2 \} \). (b) \( R_b = \{ (x, y) \mid x^2 - y^2 < 2 \} \). (c) \( R_c = \{ (x, y) \mid (x - y)^2 < 2 \} \). (d) \( R_d = \{ (x, y) \mid x \equiv y \pmod{3} \} \). **Explanation of the Task:** For each part of the exercise, you are to construct a directed graph (digraph) representing binary relations on the set \( A \). - For (a), the relation involves pairs where the squares of the elements are equal. - For (b), the relation involves pairs where the difference of the squares is less than 2. - For (c), the relation is based on the condition that the square of the difference is less than 2. - For (d), the relation checks the congruence modulo 3. Each digraph will provide a visual representation of these relations, with elements of \( A \) as nodes and the relations as directed edges between these nodes.
Transcribed Image Text:**Exercise 17.1.13.** Let \( A = \{-2, -1, 0, 1, 2\} \). Draw a digraph for each of the following binary relations on \( A \): (a) \( R_a = \{ (x, y) \mid x^2 = y^2 \} \). (b) \( R_b = \{ (x, y) \mid x^2 - y^2 < 2 \} \). (c) \( R_c = \{ (x, y) \mid (x - y)^2 < 2 \} \). (d) \( R_d = \{ (x, y) \mid x \equiv y \pmod{3} \} \). **Explanation of the Task:** For each part of the exercise, you are to construct a directed graph (digraph) representing binary relations on the set \( A \). - For (a), the relation involves pairs where the squares of the elements are equal. - For (b), the relation involves pairs where the difference of the squares is less than 2. - For (c), the relation is based on the condition that the square of the difference is less than 2. - For (d), the relation checks the congruence modulo 3. Each digraph will provide a visual representation of these relations, with elements of \( A \) as nodes and the relations as directed edges between these nodes.
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