Let X, Y be sets and f : X Y. Prove that the following are equivalent.

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Let X, Y be sets and f : X → Y. Prove that the following are equivalent.
a) f is 1-1 on X.
b) f(A\B) = f(A)\f(B) for all subsets A and B of X.
c) f-1(f(E)) = E for all subsets £ of X.
d) F(A ∩ B) = f(A) ∩ f(B) for all subsets A and B of X.

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 03:54 AM

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Let X, Y be sets and f : X Y. Prove that the following are equivalent.

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a implies b By definition fAB fAfB holds whether f is 11 or not To prove t...View the full answer

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