4. For each relation R below, determine whether it is an equivalence relation on the given set A. Also, find the requested relation class (you can do this even if R isn't an equivalence relation). (a) R= {(1,1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (3, 3), (4, 4)} on the set A = {1,2,3, 4}. Find [1]. (b) R={(x,y) E R² | x² = y²} on the set A = R. Find [5]. (c) R= {(x,y) E Z² | xy > 0} on the set A = Z. Find [-7].
4. For each relation R below, determine whether it is an equivalence relation on the given set A. Also, find the requested relation class (you can do this even if R isn't an equivalence relation). (a) R= {(1,1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (3, 3), (4, 4)} on the set A = {1,2,3, 4}. Find [1]. (b) R={(x,y) E R² | x² = y²} on the set A = R. Find [5]. (c) R= {(x,y) E Z² | xy > 0} on the set A = Z. Find [-7].
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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![4. For each relation R below, determine whether it is an equivalence relation on the given set A. Also,
find the requested relation class (you can do this even if R isn't an equivalence relation).
(a) R= {(1,1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (3, 3), (4, 4)} on the set A = {1,2,3, 4}. Find [1].
(b) R= {(x, y) E R² | x² = y²} on the set A = R. Find [5].
(c) R= {(x,y) E Z² | xy > 0} on the set A = Z. Find [–7].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cea8c15-5b49-4b58-86d0-7af488939ae5%2F8ff99bba-f9fc-4694-9dc2-f9174a4d1b27%2Fksg96cn_processed.png&w=3840&q=75)
Transcribed Image Text:4. For each relation R below, determine whether it is an equivalence relation on the given set A. Also,
find the requested relation class (you can do this even if R isn't an equivalence relation).
(a) R= {(1,1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (3, 3), (4, 4)} on the set A = {1,2,3, 4}. Find [1].
(b) R= {(x, y) E R² | x² = y²} on the set A = R. Find [5].
(c) R= {(x,y) E Z² | xy > 0} on the set A = Z. Find [–7].
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