Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 2.2, Problem 9TFQ
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Use the method of undetermined coefficients to solve the given nonhomogeneous system.
dx
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=
2x + 3y − 8
dy
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=
−x − 2y + 6
X(t) =
As discussed in Section 8.3, the Markowitz model uses the variance of the portfolio as the measure of risk. However, variance includes deviations both below and above the mean return. Semivariance includes only deviations below the mean and is considered by many to be a better measure of risk.
(a)
Develop a model that minimizes semivariance for the Hauck Financial data given in the file HauckData with a required return of 10%.
Assume
that the five planning scenarios in the Hauck Financial Services model are equally likely to occur. Hint: Modify model (8.10)–(8.19). Define a variable ds for each scenario and let
ds ≥ R − Rs
with
ds ≥ 0.
Then make the objective function:
Min
1
5
5
s = 1
ds2.
Let
FS = proportion of portfolio invested in the foreign stock mutual fund
IB = proportion of portfolio invested in the intermediate-term bond fund
LG = proportion of portfolio invested in the large-cap growth fund
LV = proportion of portfolio invested in the large-cap value fund…
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Chapter 2 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 2.1 - 5{x+2y|x{0,1,2},y{2,0,2}}Ch. 2.1 - 5{x+2y|x{0,1,2},y{2,0,2}}Ch. 2.1 - If A={a,b}, then bA.Ch. 2.1 - Prob. 4TFQCh. 2.1 - {,{}}Ch. 2.1 - {,{}}Ch. 2.1 - True/False Questions
7.
Ch. 2.1 - Prob. 8TFQCh. 2.1 - (Assume A and B are sets). ABBA.Ch. 2.1 - If A has two elements, then P(P(A)) has eight...
Ch. 2.1 - Prob. 1ECh. 2.1 - 2. List five elements in each of the following...Ch. 2.1 - Let A={1,2,3,4}. List all the subsets B of A such...Ch. 2.1 - 4. Let . Are the following statements true or...Ch. 2.1 - 5. Determine which of the following are true and...Ch. 2.1 - Prob. 6ECh. 2.1 - Determine which of the following are true and...Ch. 2.1 - Prob. 8ECh. 2.1 - a) List all the subset of set {a,b,c,d} that...Ch. 2.1 - (a) How many elements are in the power set of the...Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.2 - Prob. 1TFQCh. 2.2 - Prob. 2TFQCh. 2.2 - Prob. 3TFQCh. 2.2 - Prob. 4TFQCh. 2.2 - If A and B are setsand AB, then AB.Ch. 2.2 - Prob. 6TFQCh. 2.2 - The name of Augustus De Morgan appears in both...Ch. 2.2 - (AC)(BcAc).Ch. 2.2 - True/False Questions
9.
Ch. 2.2 - Prob. 10TFQCh. 2.2 - List A={xN|x7},B={xZ||x2|4} and C={xR|x34x=0}:...Ch. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - For A={a,b,c,{a,b}}, find (a) A{a,b} (b) {}P(A)...Ch. 2.2 - Prob. 6ECh. 2.2 - 7. Let , and . List the elements in the...Ch. 2.2 - Let n3 and A={1,2,3,.....n}. (a) How many subsets...Ch. 2.2 - Prob. 9ECh. 2.2 - 10. The universal set for this problem is the set...Ch. 2.2 - Prob. 11ECh. 2.2 - 12. Let P denote the set of primes and E the set...Ch. 2.2 - For nZ, let An={aZ|an}. Find each of the following...Ch. 2.2 - Prob. 14ECh. 2.2 - 15. Let , and .
(a) Draw a Venn diagram showing...Ch. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.3 - {(x,x+1)|xN} is a binary relation on N, the set of...Ch. 2.3 - True/False Questions
2. is a binary relation on...Ch. 2.3 - Let be a binary relation on a set A and let aA....Ch. 2.3 - Let R be a binary relation on a set A and let aA....Ch. 2.3 - Let R be a binary relation on a set A. If R is not...Ch. 2.3 - True/False Questions
6. Let be a binary relation...Ch. 2.3 - True/False Questions
7. Let be a binary relation...Ch. 2.3 - If a binary relation R is antisymmetric, then R is...Ch. 2.3 - If a binary relation R is notsymmetric, then it is...Ch. 2.3 - True/False Questions
10. Let be a binary relation...Ch. 2.3 - Let B denote the set of books in a college library...Ch. 2.3 - 2. Let A denote the set of names of streets in St....Ch. 2.3 - Determine which of the properties reflexive,...Ch. 2.3 - 4. With a table like that in Fig. 2.2, illustrate...Ch. 2.3 - 5. Let . List the ordered pairs in a relation on A...Ch. 2.3 - 6. Is it possible for a binary relation to be both...Ch. 2.3 - What is wrong with the following argument, which...Ch. 2.3 - Determine whether each of the binary relations R...Ch. 2.3 - Determine whether each of the binary relations R...Ch. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.4 - True/False Questions
“” defines an equivalence...Ch. 2.4 - An equivalence relation on a set A is a binary...Ch. 2.4 - Prob. 3TFQCh. 2.4 - Prob. 4TFQCh. 2.4 - Prob. 5TFQCh. 2.4 - Prob. 6TFQCh. 2.4 - Prob. 7TFQCh. 2.4 - Prob. 8TFQCh. 2.4 - Prob. 9TFQCh. 2.4 - Prob. 10TFQCh. 2.4 - Prob. 11TFQCh. 2.4 - Prob. 1ECh. 2.4 - 2. Explain why each of the following binary...Ch. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - For natural numbers a and b, define a~b if and...Ch. 2.4 - Prob. 7ECh. 2.4 - 8. For integers a, b, define if and only if for...Ch. 2.4 - 9. Define ~ on Z by if and only if is a multiple...Ch. 2.4 - 10. For integers a and b, define if for some...Ch. 2.4 - 11. For , define if and only if .
(a) Prove that...Ch. 2.4 - For a,bZ, define a~b if and only if a2b2 is...Ch. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Define ~ on R2 by (x,y)~(u,v) if and only if...Ch. 2.4 - Prob. 17ECh. 2.4 - Determine which of the following define...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - 22. Let A be the set of all natural numbers and ~...Ch. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.5 - A partial order on a set A is a reflexive,...Ch. 2.5 - Prob. 2TFQCh. 2.5 - True/False Questions
3. The binary relation “” on...Ch. 2.5 - Prob. 4TFQCh. 2.5 - Hasse diagrams are used to identify the...Ch. 2.5 - Prob. 6TFQCh. 2.5 - Prob. 7TFQCh. 2.5 - Prob. 8TFQCh. 2.5 - Prob. 9TFQCh. 2.5 - The statement in Question 9 is the contrapositive...Ch. 2.5 - 1. Determine whether each of the following...Ch. 2.5 - 2. (a) List the elements of the set in...Ch. 2.5 - List all pairs (x,y) with xy in the partial orders...Ch. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - In the poset (P(S),) of subsets of a set S, under...Ch. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - 10. (a) Let and, for and in A, define if and...Ch. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2 - If A={xN|x7},B={xZ||x5|3}andC={2,3}, find (AB)C.Ch. 2 - Let A={xZ|1x2},B={2x3|xA},andC={xR|x=ab,aA,bB}....Ch. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - 5. This exercise refers to the Venn diagram shown...Ch. 2 - Prob. 6RECh. 2 - Let A={1}. Find P(P(A)).Ch. 2 - Prob. 8RECh. 2 - Give an example showing that the statement...Ch. 2 - Prob. 10RECh. 2 - 11. Let A be a set.
(a) What is meant by the term...Ch. 2 - Let A={xR||x|1} and, for a,bA, define (a,b)R if...Ch. 2 - Determine whether ~ is reflexive, symmetric,...Ch. 2 - For a,bN, define a~b if and only if ab. Determine...Ch. 2 - 15. Define a relation R on Z by if is a multiple...Ch. 2 - 16. Define a relation R on Z by if is a multiple...Ch. 2 - 17. Let ~ denote an equivalence relation on a set...Ch. 2 - 18. Let ~ denote an equivalence relation on a set...Ch. 2 - Prob. 19RECh. 2 - Let A be the set of points different from the...Ch. 2 - Show that (P(Z),) is a partially ordered set.Ch. 2 - Let A={1,2,4,6,8} and, for a,bA, define a_b if and...Ch. 2 - 23. Let be a poset and . Can a and b have two...
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