Let S, T, and R be sets. Assume that f: S-» T, and g: T -» R are maps Assume that gf is onto. Does f have to be onto? Does g have to be onto? In both cases either prove that the map is onto or give a counterexample

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.3: Properties Of Composite Mappings (optional)
Problem 8E: Suppose f,g and h are all mappings of a set A into itself. a. Prove that if g is onto and fg=hg,...
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Let S, T, and R be sets. Assume that f: S-» T, and g: T -» R are maps
Assume that gf is onto. Does f have to be onto? Does g have to be onto?
In both cases either prove that the map is onto or
give a counterexample
Transcribed Image Text:Let S, T, and R be sets. Assume that f: S-» T, and g: T -» R are maps Assume that gf is onto. Does f have to be onto? Does g have to be onto? In both cases either prove that the map is onto or give a counterexample
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