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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 3.5, Problem 45ES

Textbook Problem

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Use a sequence of valid arguments to show that each argument is valid.

If the computer is not operating (~*o*), then I will not be able to finish my report (~*f*). If the office is closed (*c*), then the computer is not operating. Therefore, if I am able to finish my report, then the office is open.

To determine

**To show::**

that each argument is valid using a sequence of valid arguments.

**Given information::**

The argument "If the computer is not operating

**Concept Involved:**

__An Argument and a Valid Argument__: An argument consists of a set of statements called premises and another statement called the conclusion. An argument is valid if the conclusion is true whenever all the premises are assumed to be true. An argument is invalid if it is not a valid argument. A symbolic argument consists of a set of premises and a conclusion. It is called a symbolic argument because we generally write it in symbolic form to determine its validity.

__Standard Forms:__

Arguments can be show to be valid if they have the same symbolic form as an argument that is known to be valid.

Table 3.15 shows four symbolic forms and the name used to identify each form. Any argument that has a symbolic form identical to one of these symbolic forms is a valid argument.

Table 3.15 Standard Forms of Four Valid Arguments | ||||

Direct Reasoning | Contrapositive Reasoning | Transitive Reasoning | Disjunctive Reasoning | |

| | | | |

Table 3.16 shows to two symbolic forms associated with invalid arguments. Any argument that has one of these symbolic forms is invalid.

Table 3.16 Standard Forms of TWO Invalid Arguments | |

Fallacy of the converse | Fallacy of the inverse |

| |

Mathematical Excursions (MindTap Course List)

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Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use a truth table to determine whether the...Ch. 3.5 - Use the indicated letters to write the argument in...Ch. 3.5 - Use the indicated letters to write the argument in...Ch. 3.5 - Use the indicated letters to write the argument in...Ch. 3.5 - Use the indicated letters to write the argument in...Ch. 3.5 - 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[...Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Make use of Dc Morgans laws to write the given...Ch. 3 - Make use of Dc Morgans laws to write the given...Ch. 3 - Make use of Dc Morgans laws to write the given...Ch. 3 - Make use of Dc Morgans laws to write the given...Ch. 3 - Use a truth table to show that the given pairs of...Ch. 3 - Use a truth table to show that the given pairs of...Ch. 3 - Use a truth table to show that the given pairs of...Ch. 3 - Use a truth table to show that the given pairs of...Ch. 3 - Use a truth table to determine whether the given...Ch. 3 - Use a truth table to determine whether the given...Ch. 3 - Use a truth table to determine whether the given...Ch. 3 - Use a truth table to determine whether the given...Ch. 3 - Identify the antecedent and the consequent of each...Ch. 3 - Identify the antecedent and the consequent of each...Ch. 3 - Identify the antecedent and the consequent of each...Ch. 3 - Identify the antecedent and the consequent of each...Ch. 3 - Write each conditional statement in its equivalent...Ch. 3 - Write each conditional statement in its equivalent...Ch. 3 - Write each conditional statement in its equivalent...Ch. 3 - Write each conditional statement in its equivalent...Ch. 3 - Write the negation of each conditional statement...Ch. 3 - Write the negation of each conditional statement...Ch. 3 - Write the negation of each conditional statement...Ch. 3 - Write the negation of each conditional statement...Ch. 3 - Determine whether the given statement is true or...Ch. 3 - Determine whether the given statement is true or...Ch. 3 - Determine whether the given statement is true or...Ch. 3 - Determine whether the given statement is true or...Ch. 3 - Write each statement in If p, then q form. Every...Ch. 3 - Write each statement in If p, then q form. Being...Ch. 3 - Write each statement in If p, then q form. I could...Ch. 3 - Write each statement in If p, then q form. Being...Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - What is the inverse of the contrapositive of pq?Ch. 3 - Use the contrapositive of the following statement...Ch. 3 - Determine the original statement if the given...Ch. 3 - Determine the original statement if the given...Ch. 3 - Determine the original statement if the given...Ch. 3 - Determine the original statement if the given...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Determine whether the argument is valid or invalid...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Use an Euler diagram to determine whether the...Ch. 3 - Determine whether each sentence is a statement. a....Ch. 3 - Write the negation of each statement. Start each...Ch. 3 - Determine whether each statement is true or false....Ch. 3 - Determine the truth value of each statement given...Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Use one of De Morgans laws to write the following...Ch. 3 - What is a tautology?Ch. 3 - Write pq in its equivalent disjunctive form.Ch. 3 - Determine whether the given statement is true or...Ch. 3 - Write the a. converse, b. inverse, and c....Ch. 3 - 12. Write the symbolic form of direct reasoning.Ch. 3 - Write the symbolic form of transitive reasoning.Ch. 3 - Write the symbolic form of contrapositive...Ch. 3 - 15. Write the symbolic form of the fallacy of the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Use a truth table to determine whether the...Ch. 3 - Determine whether the argument is valid or...Ch. 3 - Determine whether the argument is valid or...Ch. 3 - Determine whether the argument is valid or...Ch. 3 - Determine whether the argument is valid or...Ch. 3 - Determine whether the argument is valid or...

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Compound Fractions Simplify the compound fractional expression. 69. x2y2x1+y1

Precalculus: Mathematics for Calculus (Standalone Book)

A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is found...

Statistics for The Behavioral Sciences (MindTap Course List)

For Problems 5-14, please provide the following information. (a) What is the level of significance? State the n...

Understanding Basic Statistics

Convert the expressions in Exercises 6584 to power form. x2y

Finite Mathematics and Applied Calculus (MindTap Course List)

Differentiating Radical functions In Exercises 3136, find the derivative of the function. See Example 7. Functi...

Calculus: An Applied Approach (MindTap Course List)

In Exercises 7-28, perform the indicated operations and simplify each expression. 25. 3(2x+13x+1)2[(3x+2)(2)(2x...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Sketch the graph of an example of a function f that satisfies all of the given conditions. limx3+f(x)=4,limx3f(...

Calculus: Early Transcendentals

Find the domain of each function. a f(x)=1ex21e1x2 b f(x)=1+xecosx

Calculus (MindTap Course List)

Use Lagrange multipliers to give an alternate solution to the indicated exercise in Section 14.7. 35. Exercise ...

Multivariable Calculus

Monotonic and Bounded Sequences In Exercises 23 and 24, determine whether the sequence with the given nth term ...

Calculus: Early Transcendental Functions

Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer betwee...

Probability and Statistics for Engineering and the Sciences

When asked to write an algebraic expression for 6 less than a number, you wrote x6, and another student wrote 6...

Intermediate Algebra

Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six dec...

Single Variable Calculus

Joyce invests $7500 in two savings accounts. One account earns interest at 4% per year; the other earns 2.5% pe...

Elementary Technical Mathematics

Convert the following decimals or whole numbers to percents.
6. 12.6

Contemporary Mathematics for Business & Consumers

a. Prove that 10n1(mod9) for every positive integer n. b. Prove that a positive integer is divisible by 9 if an...

Elements Of Modern Algebra

For each expression below, write an equivalent algebraic expression that involves x only. (For Problems 89 thro...

Trigonometry (MindTap Course List)

Find the domain and range and sketch the graph of the function h(x)=4x2.

Single Variable Calculus: Early Transcendentals

In Exercise 9 to 16, use a calculator to find the indicated cosine ratio to four decimal places. cos42

Elementary Geometry For College Students, 7e

STOCK TRANSACTIONS The stock holdings of Aaron, Betty, and Cathy at the close of trading at the beginning of th...

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False? In Exercises 87 and 88, determine whether the statement is true or false. If it is false, explai...

Calculus of a Single Variable

Rectangular-to-Polar Conversion In Exercises 1120, the rectangular coordinates of a point are given. Plot the p...

Calculus: Early Transcendental Functions (MindTap Course List)

In isosceles trapezoid MNPQ with MNQP, diagonal MPMQ. If PQ = 13 and NP = 5, how long is diagonal MP?

Elementary Geometry for College Students

Determine the sine, cosine, or tangent functions of the following angels. Round the answers to 5 decimal places...

Mathematics For Machine Technology

Which of the following structures has the larger storage capacity? a. a truncated pyramid that is 33 cubits hig...

Mathematics: A Practical Odyssey

Cars arrive at a car wash randomly and independently; the probability of an arrival is thesame for any two time...

Statistics for Business & Economics, Revised (MindTap Course List)

Describe, compare, and contrast the five research strategies (descriptive, correlational, experimental, quasi-e...

Research Methods for the Behavioral Sciences (MindTap Course List)

Refer to the following information on full-term births in the United States over a given period of time: Use th...

Introduction To Statistics And Data Analysis

A tax preparation firm is interested in comparing the quality of work at two of its regional offices. The obser...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

HOW DO YOU SEE IT? Match the general equation with its graph. Then state what axis or plane the equation is par...

Multivariable Calculus

The general solution to dydt=ky is: a) y(t) = y(0)ekt b) y(t) = y(k)et c) y(t) = y(t)ek d) y(t) = ey(0)kt

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Assume that fxis one-to-one. find f-1. fx=x3-3

College Algebra (MindTap Course List)

Finding an Equation of a Tangent PlaneIn Exercises 716, find an equation of the tangent plane to the surface at...

Calculus (MindTap Course List)

Under what circumstances would you use a multiple-baseline design instead of an ABAB (reversal) design?

Research Methods for the Behavioral Sciences (MindTap Course List)

Rewritten in reverse order,

Study Guide for Stewart's Multivariable Calculus, 8th

Logical Equivalences involving Conditional Statements | |