Let A and B be nonempty sets. Prove the following statements. (a) For any function f : A → A, if f o f is onto, then f is onto. (b) For any function f : A → B, if g : B → A is a function so that g o f = IA, then f is one-to-one.

Advanced Engineering Mathematics
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Let A and B be nonempty sets. Prove the following statements.
(a) For any function f : A → A, if f o f is onto, then f is onto.
(b) For any function f : A → B, if g : B → A is a function so that go f = IA, then f is one-to-one.
Transcribed Image Text:Let A and B be nonempty sets. Prove the following statements. (a) For any function f : A → A, if f o f is onto, then f is onto. (b) For any function f : A → B, if g : B → A is a function so that go f = IA, then f is one-to-one.
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