4. Let A = {1,2, 3, 4, 5} and let S = P(A), the power set of A. For a, b e S, define aRb if a b. (a) (8 points) Either prove that R defines an equivalence relation on S, or explain why it does not. (b) (4 points) Is R antisymmetric?

4. Let A = {1,2, 3, 4, 5} and let S = P(A), the power set of A. For a, b e S, define aRb if a b. (a) (8 points) Either prove that R defines an equivalence relation on S, or explain why it does not. (b) (4 points) Is R antisymmetric?

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

4. Let A = {1,2, 3, 4, 5} and let S = P(A), the power set of A. For a, b e S, define aRb if a C b.
(a) (8 points) Either prove that R defines an equivalence relation on S, or explain why it does not.
(b) (4 points) Is R antisymmetric?

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