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10.43. For nonempty sets A, B and C, let ƒ : A → B and g : B → C be functions. a. Prove: If go f is one-to-one, then f is one-to-one. using each of the following proof techniques: direct proof, proof by contrapositive, proof by contradiction. b. Disprove: If g o f is one-to-one, then g is one-to-one.

10.43. For nonempty sets A, B and C, let ƒ : A → B and g : B → C be functions. a. Prove: If go f is one-to-one, then f is one-to-one. using each of the following proof techniques: direct proof, proof by contrapositive, proof by contradiction. b. Disprove: If g o f is one-to-one, then g is one-to-one.

Advanced Engineering Mathematics
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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10.43

10.43. For nonempty sets A, B and C, let ƒ : A → B and g : B → C be functions. a. Prove: If go f is one-to-one, then f is one-to-one. using each of the following proof techniques: direct proof, proof by contrapositive, proof by contradiction. b. Disprove: If g o f is one-to-one, then g is one-to-one.
Transcribed Image Text:10.43. For nonempty sets A, B and C, let ƒ : A → B and g : B → C be functions. a. Prove: If go f is one-to-one, then f is one-to-one. using each of the following proof techniques: direct proof, proof by contrapositive, proof by contradiction. b. Disprove: If g o f is one-to-one, then g is one-to-one.
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