Let S = {R |R is an equivalence relation on Z+}.Prove that S 3 P(Z*).(Hint: Recall that for an equivalence relationR on Zt, we haveRC Z+ × Z+. Now what is the relationshipbetween S andP(Z+ × Z+)? What is the relationshipbetween power sets of two sets which havethe same cardinality?)

Let A, B and C are the sets. For reflexive , Let a∈A , A⊂-A It is reflexive. Let A⊂-B and B⊂-C ,…

Answered: Let S = {R| R is an equivalence…

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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Question

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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