(Discrete Math) Which one of the following statements is a true statement?O If f:AB and g:B→ C are functions and g •f is one-to-one, g must be one-to-one.>O If f:A→ B and g:B→ C are functions and gof is onto, ƒ must be onto.O If f:A» B and g:B→ C are functions and g• f is one-to-one, f must be one-to-one.O If f:A -→ B and g:B→ C are functions and g•f is one-to-one, f must be onto.

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Which one of the following statements is a true statement? O If f:A » B and g:B → C are functions and g o f is one-to-one, g must be one-to-one. O If f:A – » B and g:B → C are functions and g o f is onto, f must be onto. O If f:A → B and g:B » C are functions and gof is one-to-one, f must be one-to-one. O If f:A → B and g:B - → C are functions and g • f is one-to-one, f must be onto.

Which one of the following statements is a true statement? O If f:A » B and g:B → C are functions and g o f is one-to-one, g must be one-to-one. O If f:A – » B and g:B → C are functions and g o f is onto, f must be onto. O If f:A → B and g:B » C are functions and gof is one-to-one, f must be one-to-one. O If f:A → B and g:B - → C are functions and g • f is one-to-one, f must be onto.

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 12E: Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.

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