WS-11-9-2010

WS-11-9-2010 - f ◦ g = I B Give an example of nonempty...

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In the following two problems A and B are arbitrary nonempty sets. Let f : A B and g : B A such that g f = I A . Prove that if f is onto, then f g = I B . 1. Prove by example that ( g f = I A and f is one-to-one) does not imply f g = I B . Let f : A B and g : B A such that g f = I A . Prove that if g is one-to-one, then 2. f g = I B . Prove by example that ( g f = I A and g is onto) does not imply
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Unformatted text preview: f ◦ g = I B . Give an example of nonempty sets A and B and functions f : A → B and g : B → A such 3. that g ◦ f = I A but f ◦ g 6 = I B . [Hint: The first two problems seriously restrict the possible choices for f and g .]...
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