Let A and B be two nonempty sets, f: A B be a function and R be an equivalencerelation on the set B. For x1, x2 e A, we putxRx2 if and only if f(x1)Rf(x2).Show that R' is an equivalence relation on the set A.

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Answered: Let A and B be two nonempty sets, f: A…

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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This question confuses me, I dont get what is being asked? How do I approach this? "Let A be a nonempty set and let B be a subset of the power set P(A) of A. Define a relation R from A to B byxRY if x ∈ Y. Give an example of two sets A and B that illustrate this. What is R for these two sets?"

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Let A and B be two nonempty sets, f: A → B be a function and R be an equivalence relation on the set B. For r1, c2 E A, we put xRx2 if and only if f(x1)Rf(x2). Show that R' is an equivalence relation on the set A.