be an equivalence relation on the set A = {1, 2,...,8}, and denote the equivalence class of x E A by [x]. Let - (a) Suppose that 1 € [3], 4 € [2], and 2 € [1]. Prove that [4] = [3]. (b) Ignore part (a) and suppose now that If |1| has 2 elements, |2| has 3 elements, 1 ~ 6, 2 ~ 5, and 7 ~ 5, has 3 equivalence classes. then i. Write - as a set of ordered pairs. ii. Find the partition of A determined by
be an equivalence relation on the set A = {1, 2,...,8}, and denote the equivalence class of x E A by [x]. Let - (a) Suppose that 1 € [3], 4 € [2], and 2 € [1]. Prove that [4] = [3]. (b) Ignore part (a) and suppose now that If |1| has 2 elements, |2| has 3 elements, 1 ~ 6, 2 ~ 5, and 7 ~ 5, has 3 equivalence classes. then i. Write - as a set of ordered pairs. ii. Find the partition of A determined by
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 - be an equivalence relation on the set A = {1,2,...,8}, and
denote the equivalence class of x E A by [x].
(a) Suppose that 1 € [3], 4 € [2], and 2 e [1]. Prove that [4] = [3].
(b) Ignore part (a) and suppose now that - has 3 equivalence classes.
If [1] has 2 elements, [2] has 3 elements, 1 ~ 6, 2 ~ 5, and 7~ 5,
then
i. Write - as a set of ordered pairs.
ii. Find the partition of A determined by](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16587444-2baf-4a64-89bf-0dbc007ed50f%2F797e5241-0959-40f5-bdc9-83d53c3a86d0%2F45pcdl_processed.png&w=3840&q=75)
Transcribed Image Text:Let - be an equivalence relation on the set A = {1,2,...,8}, and
denote the equivalence class of x E A by [x].
(a) Suppose that 1 € [3], 4 € [2], and 2 e [1]. Prove that [4] = [3].
(b) Ignore part (a) and suppose now that - has 3 equivalence classes.
If [1] has 2 elements, [2] has 3 elements, 1 ~ 6, 2 ~ 5, and 7~ 5,
then
i. Write - as a set of ordered pairs.
ii. Find the partition of A determined by
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