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1. Define a function f : Z x Z → Z by f(m, n) = 2n – 4m. (a) Prove that ƒ is not one-to-one. (b) Prove that the range of f is equal to the even numbers. In other words, show rng f = {2k|k E Z}, by using the usual methods for proving an equality of sets.

1. Define a function f : Z x Z → Z by f(m, n) = 2n – 4m. (a) Prove that ƒ is not one-to-one. (b) Prove that the range of f is equal to the even numbers. In other words, show rng f = {2k|k E Z}, by using the usual methods for proving an equality of sets.

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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1. Define a function f : Z x Z → Z by f(m, n) = 2n – 4m. (a) Prove that ƒ is not one-to-one. (b) Prove that the range of f is equal to the even numbers. In other words, show rng f = {2k|k E Z}, by using the usual methods for proving an equality of sets.
Transcribed Image Text:1. Define a function f : Z x Z → Z by f(m, n) = 2n – 4m. (a) Prove that ƒ is not one-to-one. (b) Prove that the range of f is equal to the even numbers. In other words, show rng f = {2k|k E Z}, by using the usual methods for proving an equality of sets.
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