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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 2: Q14E (page 153)

Determine whether $f : Z \times Z \to Z$ is onto if
$f (m, n) = 2 m - n$
role="math" localid="1668412540074" $f (m, n) = m^{2} - n^{2}$
$f (m, n) = m + n + 1$
$f (m, n) = |m| - |n|$
$f (m, n) = m^{2} - 4$

Short Answer

Expert verified

Onto
Not onto
Onto
onto
onto

Step by step solution

Step: 1

Onto
Not onto
Onto
onto
onto

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Most popular questions from this chapter

Question: Specify a codomain for each of the functions in Exercise 17. Under what conditions is each of the functions with the codomain you specified onto?

Show that $\sum_{j}^{n} (a_{j} - a_{j - 1}) = a_{n} - a_{0}, where a_{0}, a_{1}, \dots . . a_{n}$ , is a sequence of real numbers. This type of sum is called telescoping.

Specify a codomain for each of the functions in Exercise 17. Under what conditions is each of the functions with the codomain you specified onto?

Sum both sides of the identity $k^{2} - (k - 1)^{2} = 2 k - 1 from k = 1 to k = n$ to and use Exercise 35 to find

a) a formula for $\sum_{k = 1}^{n} (2 k - 1)$ (the sum of the first n odd natural numbers).

b) a formula for $\sum_{k = 1}^{n} k$

a) Define the inverse of a function

b) When does a function have an inverse?

C) Does the function $f (n) = 10 - n$ from the set of integers to the set of integers have an inverse? If so, what is it?

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Determine whether $f : Z \times Z \to Z$ is onto if
$f (m, n) = 2 m - n$
role="math" localid="1668412540074" $f (m, n) = m^{2} - n^{2}$
$f (m, n) = m + n + 1$
$f (m, n) = |m| - |n|$
$f (m, n) = m^{2} - 4$

Short Answer

Step by step solution

Step: 1

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Most popular questions from this chapter

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Determine whether f:Z×Z→Zis onto iffm,n=2m-nrole="math" localid="1668412540074" fm,n=m2-n2fm,n=m+n+1fm,n=m-nfm,n=m2-4

Short Answer

Step by step solution

Step: 1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Decision Maths

Geometry

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Determine whether $f : Z \times Z \to Z$ is onto if
$f (m, n) = 2 m - n$
role="math" localid="1668412540074" $f (m, n) = m^{2} - n^{2}$
$f (m, n) = m + n + 1$
$f (m, n) = |m| - |n|$
$f (m, n) = m^{2} - 4$