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7. Let A and B be sets, and let f: A → B and g: B → A be functions. Suppose that: • go f(a) = a for every a € A; ● fog(b) = b for every b € B. Prove that f is bijective.

7. Let A and B be sets, and let f: A → B and g: B → A be functions. Suppose that: • go f(a) = a for every a € A; ● fog(b) = b for every b € B. Prove that f is bijective.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...
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7. Let A and B be sets, and let f: A → B and g: B –→ A be functions. Suppose that: • go f(a) = a for every a E A; fo g(b) : = b for every b E B. Prove that f is bijective.
Transcribed Image Text:7. Let A and B be sets, and let f: A → B and g: B –→ A be functions. Suppose that: • go f(a) = a for every a E A; fo g(b) : = b for every b E B. Prove that f is bijective.
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