Define a relation on N x N as follows: (a, b) R (c, d) ⇒a+d=b+c (2.1) Is (3, 6) R (3, 5)? Explain. (2.2) Is (1, 1) R (3, 5)? Explain. (2.3) Prove that R is an equivalence relation.
Define a relation on N x N as follows: (a, b) R (c, d) ⇒a+d=b+c (2.1) Is (3, 6) R (3, 5)? Explain. (2.2) Is (1, 1) R (3, 5)? Explain. (2.3) Prove that R is an equivalence relation.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 28E
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![Define a relation on Nx N as follows:
(a, b) R (c, d) ⇒a+d=b+c
(2.1) Is (3, 6) R (3, 5)? Explain.
(2.2) Is (1, 1) R. (3, 5)? Explain.
(2.3) Prove that R is an equivalence relation.
(2.4) List 3 elements that belong to the equivalence class
[(1, 2)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3491c8b3-b740-49e2-9489-50e982fb3ce6%2F49b7b4e8-7911-4528-818c-31182df6838d%2F44vx1uq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Define a relation on Nx N as follows:
(a, b) R (c, d) ⇒a+d=b+c
(2.1) Is (3, 6) R (3, 5)? Explain.
(2.2) Is (1, 1) R. (3, 5)? Explain.
(2.3) Prove that R is an equivalence relation.
(2.4) List 3 elements that belong to the equivalence class
[(1, 2)].
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