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Z defined by f(n) s injective but not surjec 5 surjective but not injec

Z defined by f(n) s injective but not surjec 5 surjective but not injec

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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Decide whether each of the following functions is injective and/or surjective. f:Z Z defined by f(n) = n. O f is injective but not surjective O f is surjective but not injective Ofis both injective and surjective Of is neither injective nor surjective. g: Zx Z Z x Z defined by f(m, n) – (2m, m + n). O g is injective but not surjective Og is surjective but not injective O gis both injective and surjective Ogis neither injective nor surjective. h:N Ndefined by (n)-the sum of the digits of n. Chisinjective but not surjective Chissurjective but not injective his both injective and surjective his neitherinjective nor surjective.
Transcribed Image Text:Decide whether each of the following functions is injective and/or surjective. f:Z Z defined by f(n) = n. O f is injective but not surjective O f is surjective but not injective Ofis both injective and surjective Of is neither injective nor surjective. g: Zx Z Z x Z defined by f(m, n) – (2m, m + n). O g is injective but not surjective Og is surjective but not injective O gis both injective and surjective Ogis neither injective nor surjective. h:N Ndefined by (n)-the sum of the digits of n. Chisinjective but not surjective Chissurjective but not injective his both injective and surjective his neitherinjective nor surjective.
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