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
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 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
Solving this equation for n1 and simplifying the result gives that
Therefore, F is
2 − 3n1 =
n1 =
.
(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.
is not an integer. Thus, F is not onto.
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