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 1 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 1.1 - True/False Questions
“” means “”
Ch. 1.1 - A truth table based on four simple statements...Ch. 1.1 - True/False Questions
2. If is true, then is also...Ch. 1.1 - If p and q are both false, the truth value of...Ch. 1.1 - If pq is false, the truth value of (pq)(pq) is...Ch. 1.1 - pq andqp are logically equivalent.Ch. 1.1 - True/False Questions
7. A statement and its...Ch. 1.1 - (pq)(pq) is a tautology.Ch. 1.1 - True/False Questions
9. If B is a tautology and A...Ch. 1.1 - True/False Questions
10. If A and B are both...
Ch. 1.1 - Construct a truth table for each of the following...Ch. 1.1 - (a) If pq is false, determine the truth value of...Ch. 1.1 - 3. Determine the truth value for
when are all...Ch. 1.1 - 4. Repeat Exercise 3 in the case where are all...Ch. 1.1 - 5. (a) Show that is a tautology.
(b) Show that ...Ch. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - 10. (a) Show that the statement is not logically...Ch. 1.1 - 11. If and are statements, then the compound...Ch. 1.2 - True/False Questions
Two statements A and B are...Ch. 1.2 - True/False Questions
2. “A B” and “A B” mean the...Ch. 1.2 - True/False Questions
3. () () for any statement ....Ch. 1.2 - True/False Questions
4. for any statements
Ch. 1.2 - (p(qr))((pq)(pr)) for any statements p,q,r.Ch. 1.2 - ((pq))((p)(q)) for any statements p,q.Ch. 1.2 - If A Band C is any statement, then (A C) (B ...Ch. 1.2 - True/False Questions
8. is in disjunctive normal...Ch. 1.2 - (pq(r))((p)(q)(r)) is in disjunctive normal form.Ch. 1.2 - True/False Questions
10. Disjunctive normal form...Ch. 1.2 - Prob. 1ECh. 1.2 - (a) Show that p[(pq)] is a tautology. (b) What is...Ch. 1.2 - Simplify each of the following statements. (a)...Ch. 1.2 - 4. Using truth tables, verify the following...Ch. 1.2 - 5. Using the properties in the text together with...Ch. 1.2 - Prove that the statements (p(q))q and (p(q))p are...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Express each of the following statements in...Ch. 1.2 - Find out what you can about Augustus De Morgan and...Ch. 1.3 - True/False Questions
An argument is valid if,...Ch. 1.3 - Prob. 2TFQCh. 1.3 - Prob. 3TFQCh. 1.3 - True/False Questions
4. De Morgan’s laws are two...Ch. 1.3 - The chain rule has pq and qr as its premises.Ch. 1.3 - Prob. 6TFQCh. 1.3 - Prob. 7TFQCh. 1.3 - Prob. 8TFQCh. 1.3 - Prob. 9TFQCh. 1.3 - Prob. 10TFQCh. 1.3 - Determine whether or not each of the following...Ch. 1.3 - 2. Verify that each of the five rules of inference...Ch. 1.3 - Verify that each of the following arguments is...Ch. 1.3 - Test the validity of each of the following...Ch. 1.3 - 5. Determine the validity of each of the following...Ch. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - 10. What language is being used when we say “modus...Ch. 1 - Construct a truth table for the compound statement...Ch. 1 - Determine the truth value of [p(q((r)s))](rt),...Ch. 1 - 3. Determine whether each statement is a...Ch. 1 - Two compound statements A and B have the property...Ch. 1 - 5. (a) Suppose A, B, and C are compound statements...Ch. 1 - Establish the logical equivalence of each of the...Ch. 1 - 7. Express each of the following statements in...Ch. 1 - Determine whether each of the following arguments...Ch. 1 - Discuss the validity of the argument pq(p)r Purple...Ch. 1 - 10. Determine the validity of each of the...
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- Let the universal set be whole numbers 1 through 20 inclusive. That is, U = {1, 2, 3, 4, . . ., 19, 20}. Let A, B, and C be subsets of U. Let A be the set of all prime numbers: A = {2, 3, 5, 7, 11, 13, 17, 19} Let B be the set of all odd numbers: B = {1,3,5,7, . . ., 17, 19} Let C be the set of all square numbers: C = {1,4,9,16}arrow_forwardA research team consists of 4 senior researchers and 10 research assistants. The team needs to select 2 senior researchers and 2 research assistants to attend a conference. How many different ways can the group being sent to the conference be formed?arrow_forwardThere are 25 different varieties of flowering plants found in a natural habitat you are studying. You are asked to randomly select 5 of these flowering plant varieties to bring back to your laboratory for further study. How many different combinations of are possible? That is, how many possible 5 plant subgroups can be formed out of the 25 total plants found?arrow_forward
- A person is tossing a fair, two-sided coin three times and recording the results (either a Heads, H, or a Tails, T). Let E be the event that exactly two heads are tossed. Which of the following sets represent the event E? Group of answer choices {HHT, HTH, THH} {HHT, THH} {HHH, HHT, HTH, THH, TTT, TTH, THT, HTT} {HH}arrow_forwardTake Quiz 54m Exit Let the universal set be whole numbers 1 through 20 inclusive. That is, U = {1, 2, 3, 4, . . ., 19, 20}. Let A, B, and C be subsets of U. Let A be the set of all prime numbers: A = {2, 3, 5, 7, 11, 13, 17, 19} Let B be the set of all odd numbers: B = {1,3,5,7, • • , 17, 19} Let C be the set of all square numbers: C = {1,4,9,16} ☐ Question 2 3 pts Which of the following statement(s) is true? Select all that apply. (1) АСВ (2) A and C are disjoint (mutually exclusive) sets. (3) |B| = n(B) = 10 (4) All of the elements in AC are even numbers. ☐ Statement 1 is true. Statement 2 is true. Statement 3 is true. Statement 4 is true.arrow_forward☐ Question 1 2 pts Let G be the set that represents all whole numbers between 5 and 12 exclusive. Which of the following is set G in standard set notation. (Roster Method)? O G = [5, 12] G = {5, 6, 7, 8, 9, 10, 11, 12} O G = (5, 12) OG = {6, 7, 8, 9, 10, 11}arrow_forward
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