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Consider two functions f : X → Y and g : Y → Z. Decide whether each of the following statements is true or false, and prove each claim. a) If g • f is injective, then g is injective. b) If g • f is injective, then f is injective. c) If g • f is injective and f is surjective, then g is injective.

Consider two functions f : X → Y and g : Y → Z. Decide whether each of the following statements is true or false, and prove each claim. a) If g • f is injective, then g is injective. b) If g • f is injective, then f is injective. c) If g • f is injective and f is surjective, then g is injective.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider two functions f : X → Y and g : Y → Z. Decide whether each of the following statements is true or false, and prove each claim. a) If g • f is injective, then g is injective. b) If g • f is injective, then f is injective. c) If g • f is injective and f is surjective, then g is injective.
Transcribed Image Text:Consider two functions f : X → Y and g : Y → Z. Decide whether each of the following statements is true or false, and prove each claim. a) If g • f is injective, then g is injective. b) If g • f is injective, then f is injective. c) If g • f is injective and f is surjective, then g is injective.
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