Answered: Proposition 2.12. Suppose- that R is an…

Proposition 2.12. Suppose- that R is an equivalence relation on a set A, and let a, b e A. Then the following are equivalent. (i) a ~b (i) a E (b) (iii) [a] n (b] + 0 (iv) [a] = [b]

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

Proposition 2.12. Suppose that R is an equivalence relation on a set A, and let a, bEA.
Then the following are equivalent.
(2) a ~b
9.
(i) a E [b
(iii) [a] n [b] # Ø
(iv) [a] = [b]
%3|

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