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Decide whether each of the following functions is injective and/or surjective. f: N N defined by f(n) = n +1. Of is injective but not surjective Of is surjective but not injective Of is both injective and surjective Of is neither injective nor surjective. g: RxR RxR defined by f(m, n) = (m + n, m – n). Og is injective but not surjective g is surjective but not injective Og is both injective and surjective g is neither injective nor surjective. h: N (0, 1,2,3,4,5,6, 7,8,9} defined by h(n) = the last digit of n2. h is injective but not surjective h is surjective but not injective Oh is both injective and surjective h is neither injective nor surjective.

Decide whether each of the following functions is injective and/or surjective. f: N N defined by f(n) = n +1. Of is injective but not surjective Of is surjective but not injective Of is both injective and surjective Of is neither injective nor surjective. g: RxR RxR defined by f(m, n) = (m + n, m – n). Og is injective but not surjective g is surjective but not injective Og is both injective and surjective g is neither injective nor surjective. h: N (0, 1,2,3,4,5,6, 7,8,9} defined by h(n) = the last digit of n2. h is injective but not surjective h is surjective but not injective Oh is both injective and surjective h is neither injective nor surjective.

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: N N defined by f(n) = n+ 1. Of is injective but not surjective Of is surjective but not injective Of is both injective and surjective Of is neither injective nor surjective. g : RxR RxR defined by f(m, n) = (m + n, m – n). g is injective but not surjective g is surjective but not injective g is both injective and surjective g is neither injective nor surjective. h: N (0, 1,2, 3,4,5,6, 7, 8,9} defined by h(n) = the last digit of n2. Oh is injective but not surjective Oh is surjective but not injective h is both injective and surjective h is neither injective nor surjective.
Transcribed Image Text:Decide whether each of the following functions is injective and/or surjective. f: N N defined by f(n) = n+ 1. Of is injective but not surjective Of is surjective but not injective Of is both injective and surjective Of is neither injective nor surjective. g : RxR RxR defined by f(m, n) = (m + n, m – n). g is injective but not surjective g is surjective but not injective g is both injective and surjective g is neither injective nor surjective. h: N (0, 1,2, 3,4,5,6, 7, 8,9} defined by h(n) = the last digit of n2. Oh is injective but not surjective Oh is surjective but not injective h is both injective and surjective h is neither injective nor surjective.
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