In Discrete Math (a) Define F: Z → Z by the rule F(n) = 2 − 3n, for each integer n.   (i) Is F one-to-one?   Suppose n1 and  n2 are any integers, such that F(n1) = F(n2). Substituting from the definition of F gives that  2 − 3n1 =     Solving this equation for n1 and simplifying the result gives that  n1 =     Therefore, F is       . (ii) Show that F is not onto.   Counterexample:   Let m = 1    For this value of m, the only number n with the property that F(n) = m

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 30E
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In Discrete Math
(a) Define FZ → Z by the rule F(n) = 2 − 3n, for each integer n.
 
(i) Is F one-to-one?
 
Suppose n1 and  n2 are any integers, such that F(n1) = F(n2). Substituting from the definition of F gives that 
2 − 3n1
 
 Solving this equation for n1 and simplifying the result gives that 
n1
 
 Therefore, F is  
    .
(ii) Show that F is not onto.
 
Counterexample:
 
Let m = 1
 
 For this value of m, the only number n with the property that F(n) = m
 is not an integer. Thus, F is not onto.
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