Discrete Mathematics
Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 1.2, Problem 30E
To determine

To show: The identity P(n,2)=n2−n, for n>1.

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Chapter 1 Solutions

Discrete Mathematics

Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - use the PERT method to determine the total project...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...
Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - In Exercises 9–16, a table is given telling the...Ch. 1.1 - A small purse manufacturer has a single machine...Ch. 1.1 - What is the answer to the previous problem if the...Ch. 1.1 - A survey is to be made of grocery shoppers in Los...Ch. 1.2 - In Exercises 1–16, calculate the number...Ch. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - In Exercises 1–16, calculate the number...Ch. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - In Exercises 1-16, calculate the number...Ch. 1.2 - A baseball manager has decided who his 9 starting...Ch. 1.2 - A president, vice president, and treasurer are to...Ch. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Different prizes for first place, second place,...Ch. 1.2 - Prob. 23ECh. 1.2 - A farmer with 7 cows likes to milk them in a...Ch. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - A dinner special for 4 diners at a Chinese...Ch. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Show that if 0 ≤ 2r ≤ n, then . Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Exercises 1–14, let A= {1, 2}, B = {2, 3, 4}, C =...Ch. 1.3 - Suppose that the rating/kilogram ratio is computed...Ch. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - How many subsets does {Dopey, Happy, …, Doc}...Ch. 1.3 - How many subsets does {Chico, Harpo, Groucho,...Ch. 1.3 - Prob. 24ECh. 1.3 - Suppose m and n are positive integers with m < n....Ch. 1.3 - Prob. 26ECh. 1.3 - A draw poker player may discard some of his 5...Ch. 1.3 - Suppose that in the previous problem no more than...Ch. 1.3 - How long would it take a computer that can check...Ch. 1.3 - Find a subset of the 12 experiments with a total...Ch. 1.4 - In Exercises 1–6, tell whether the given...Ch. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - In Exercises 1–6, tell whether the given...Ch. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - Prob. 13ECh. 1.4 - In Exercises 11–14, tell what next string will be...Ch. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - In Exercises 15–18, make a table listing the...Ch. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - In Exercises 19–22, illustrate as in Example 1.5...Ch. 1.4 - In Exercises 19–22, illustrate as in Example 1.5...Ch. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - In Exercises 23–26, estimate how long a computer...Ch. 1.4 - In Exercises 27–30, tell how many elementary...Ch. 1.4 - In Exercises 27–30, tell how many elementary...Ch. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1 - Prob. 1SECh. 1 - Prob. 2SECh. 1 - Prob. 3SECh. 1 - Prob. 4SECh. 1 - Prob. 5SECh. 1 - Prob. 6SECh. 1 - Prob. 7SECh. 1 - Prob. 8SECh. 1 - Prob. 9SECh. 1 - Prob. 10SECh. 1 - Prob. 11SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 13SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 15SECh. 1 - Let A = {1, 3, 5}, B = {2, 6, 10}, and C = {x: x...Ch. 1 - Prob. 17SECh. 1 - In Cincinnati, chili consists of spaghetti topped...Ch. 1 - Five students decide to send a delegation to a...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20–23, tell whether each expression...Ch. 1 - In Exercises 20-23, tell whether each expression...Ch. 1 - Let P(x) = 3x3+4x−5. Compute the various values S...Ch. 1 - Repeat the previous problem, using Horner's...Ch. 1 - Let S = {1, 2, 3, 4}. Find the ordered sequence of...Ch. 1 - Illustrate the use of the bubble sort algorithm to...Ch. 1 - How long would it take a computer to do 25!...Ch. 1 - Apply the following algorithm to n = 18. What is...Ch. 1 - Prob. 30SECh. 1 - Prob. 1CPCh. 1 - Prob. 2CPCh. 1 - Prob. 3CPCh. 1 - Prob. 4CPCh. 1 - Prob. 5CPCh. 1 - Prob. 6CPCh. 1 - Prob. 9CPCh. 1 - Prob. 10CP
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