Let A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by: xRy ⇔ |x| = |y|, where | · | denotes the set cardinality. (i) Prove that R is an equivalence relation. (ii) Find all equivalence classes for the case A = {1, 2, 3}.

Let A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by: xRy ⇔ |x| = |y|, where | · | denotes the set cardinality. (i) Prove that R is an equivalence relation. (ii) Find all equivalence classes for the case A = {1, 2, 3}.

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 A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by:
xRy ⇔ |x| = |y|,
where | · | denotes the set cardinality.
(i) Prove that R is an equivalence relation.
(ii) Find all equivalence classes for the case A = {1, 2, 3}.

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