Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true?(Hint: The equivalence classes of an equivalence relation on A gives apartition of A, or in other words, their union is A and they are pairwisedisjoint.)There is an equivalence relation on A whose equivalence classes are:O {1,2},{3,5},{6}.There is an equivalence relation on A whose equivalence classes are:{1,2, 3}, {3, 5}, {4, 6}.There is an equivalence relation on A whose equivalence classes are:O {1,2,3}, {5},{5,6}.There is an equivalence relation on A whose equivalence classes are:{1,2, 3}, {5}, {4,6}.

Equivalence classes: Let A be a nonempty set. Let R be the equivalence relation defined on A. Let…

Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an equivalence relation on A gives a partition of A, or in other words, their union is A and they are pairwise disjoint.) There is an equivalence relation on A whose equivalence classes are: {1,2},{3,5}, {6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {3, 5}, {4,6}. There is an equivalence relation on A whose equivalence classes are: {1,2,3}, {5}, {5,6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {5}, {4,6}.

Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an equivalence relation on A gives a partition of A, or in other words, their union is A and they are pairwise disjoint.) There is an equivalence relation on A whose equivalence classes are: {1,2},{3,5}, {6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {3, 5}, {4,6}. There is an equivalence relation on A whose equivalence classes are: {1,2,3}, {5}, {5,6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {5}, {4,6}.

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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A: Introduction :

Question

Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true?
(Hint: The equivalence classes of an equivalence relation on A gives a
partition of A, or in other words, their union is A and they are pairwise
disjoint.)
There is an equivalence relation on A whose equivalence classes are:
O {1,2},{3,5},{6}.
There is an equivalence relation on A whose equivalence classes are:
{1,2, 3}, {3, 5}, {4, 6}.
There is an equivalence relation on A whose equivalence classes are:
O {1,2,3}, {5},{5,6}.
There is an equivalence relation on A whose equivalence classes are:
{1,2, 3}, {5}, {4,6}.

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