Open In App

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 2: Q18SE (page 187)

Show that if nis an integer, then n= _n/2_ + _n/2_.

Short Answer

Expert verified

The statement is true

Step by step solution

Step 1:

If n is even, n/2 is an integer and the floor and ceiling functions give n/2 each. Hence it is true for even n. If n is odd, let n = k+1, where k is even.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a teacher his or her

Office
Assigned bus to chaperone in a group of buses taking students on a field trip
Salary
Social security number

let $f (x) = 2 x$ where the domain is the set of real numbers. What is

$f (Z)$ ?
$f (N)$ ?
$f (R)$ ?

Suppose that f is an invertible function from Y to Z and g is an invertible function from X to Y. Show that the inverse of the composition f $\circ$ g is given by $(f \circ g)^{- 1} = g^{- 1} \circ f^{- 1}$

Draw the graph of these functions.

$\begin{aligned} (a) f (x) = ⌊ x + 1 / 2 ⌋ \\ (b) f (x) = ⌊ 2 x + 1 ⌋ \\ (c) f (x) = ⌊ x / 3 ⌋ \\ (d) f (x) = ⌈ 1 / x ⌉ \\ (e) f (x) = ⌈ x - 2 ⌉ + ⌊ x + 2 ⌋ \\ (f) f (x) = ⌊ 2 x ⌋ ⌈ x / 2 ⌉ \\ (g) f (x) = ⌈ ⌊ x - 1 / 2 ⌋ + 1 / 2 ⌉ \end{aligned}$

Compute each of these double sums

\begin{aligned} \sum_{i = 1}^{2} \sum_{j = 1}^{3} (i + j) \\ \sum_{i = 0}^{2} \sum_{j = 0}^{3} (2 i + 3 j) \\ \sum_{i = 1}^{3} \sum_{j = 0}^{2} i \\ \sum_{i = 0}^{2} \sum_{j = 1}^{3} ij \end{aligned}

See all solutions

Recommended explanations on Math Textbooks

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

Show that if nis an integer, then n= _n/2_ + _n/2_.

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

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Company

Product

Help