Let S = {R| R is an equivalence relation on z†}. Prove that S 3 P(Z+). (Hint: Recall that for an equivalence relation R on ZT, we have RC Z+ × Z+. Now what is the relationship
Let S = {R| R is an equivalence relation on z†}. Prove that S 3 P(Z+). (Hint: Recall that for an equivalence relation R on ZT, we have RC Z+ × Z+. Now what is the relationship
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 S = {R |
R is an equivalence relation on Z+}.
Prove that S 3 P(Z*).
(Hint: Recall that for an equivalence relation
R on Zt, we have
RC Z+ × Z+. Now what is the relationship
between S and
P(Z+ × Z+)? What is the relationship
between power sets of two sets which have
the same cardinality?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59877b05-660b-4a35-a518-f3aba2587522%2Fa458bfd4-59f1-4639-b68b-e7df98c8a5b8%2Fkwqip1b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let S = {R |
R is an equivalence relation on Z+}.
Prove that S 3 P(Z*).
(Hint: Recall that for an equivalence relation
R on Zt, we have
RC Z+ × Z+. Now what is the relationship
between S and
P(Z+ × Z+)? What is the relationship
between power sets of two sets which have
the same cardinality?)
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