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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 3.5, Problem 47ES

Textbook Problem

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Use all of the premises to determine a valid conclusion for the given argument.

To determine

**To identify::**

A valid conclusion for the given argument using all the premises.

**Given information::**

The argument in symbolic form

**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 |

| |

Logical Equivalences involving Conditional Statements | |

Mathematical Excursions (MindTap Course List)

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[...Ch. 3.3 - Construct a truth table for the given Statement. [...Ch. 3.3 - Construct a truth table for the given Statement....Ch. 3.3 - Construct a truth table for the given Statement. [...Ch. 3.3 - Construct a truth table for the given Statement. [...Ch. 3.3 - Construct a truth table for the given Statement. [...Ch. 3.3 - Construct a truth table for the given Statement. {...Ch. 3.3 - Construct a truth table for the given Statement. [...Ch. 3.3 - Construct a truth table for the given Statement. 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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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a A projectile is fired from the origin down an inclined plane that makes an angle with the horizontal. The an...

Calculus (MindTap Course List)

Critical Thinking You are given the information that P(A) = 0.30 and P(B) = 0.40. (a) Do you have enough inform...

Understanding Basic Statistics

Find f'(a). f(x)=12x

Calculus: Early Transcendentals

Define the terms population and sample, and explain the role of each in a research study.

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

Operations with Vectors Find 2u, 3v, u + v, and 3u 4v for the given vectors u and v. 34. u = i, v = 2j

Precalculus: Mathematics for Calculus (Standalone Book)

Driving Costs A study of the costs of driving 2012 smallsized sedans found that the average cost per mile (car ...

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

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Applied Calculus

Writing the Terms of a Sequence In Exercises 1-4, write the first five terms of the sequence with the given nth...

Calculus: Early Transcendental Functions

Find the remaining trigonometric ratios. 32. cosx=13,x32

Single Variable Calculus: Early Transcendentals, Volume I

The completion time X for a certain task has cdf F(x) given by {0x0x330x1112(73x)(7434x)1x731x73 a. Obtain the ...

Probability and Statistics for Engineering and the Sciences

Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate college students to examine their weight status, healt...

Statistics for The Behavioral Sciences (MindTap Course List)

Solve the equations in Exercises 126. 2x3x12x+3x+1=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Cost The marginal cost for manufacturing an electrical component is $7.75 per unit, and the fixed cost is $500....

Calculus: An Applied Approach (MindTap Course List)

A variety of information has been collected for all district high schools. Find the most appropriate measure of...

Essentials Of Statistics

Draw the graph of the line through the given point with the given slope: (2,7),m=1

Elementary Technical Mathematics

Problems 107 through 112 refer to right triangle ABC in which C=90. Solve each triangle. a=4.37, c=6.21

Trigonometry (MindTap Course List)

Two new workers were hired for an assembly line. Jim processed 25 units during the first hour and 45 units duri...

Single Variable Calculus: Early Transcendentals

Assuming that all net sales figures are at retail and all cost of goods sold figures are at cost, calculate the...

Contemporary Mathematics for Business & Consumers

In Review Exercises 7 to 13, sketch and describe the locus in a plane. Find the locus of points that are 1 in. ...

Elementary Geometry For College Students, 7e

14. Let be an ideal in a ring with unity . Prove that if then .

Elements Of Modern Algebra

In Exercises 58, determine whether the events A and B are independent. 7.P(A)=.5, P(B)=.7, P(AB)=.85

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding the Slope and y-Intercept In Exercises 2934, find the slope and the y-intercept (if possible) of the li...

Calculus of a Single Variable

In Exercises 17 to 30, use the formula A=12aP to find the area of the regular polygon described. Find the area ...

Elementary Geometry for College Students

Volume Let R be a region in the xy-plane whose area is B. When f(x,y)=k for every point (x, y) in R, what is th...

Calculus: Early Transcendental Functions (MindTap Course List)

Find the unknown area, length, or width for each of the rectangles 31 through 42. Where necessary, round the an...

Mathematics For Machine Technology

Find the probability of drawing the hand described in Exercise 72. Exercise 72: In how many ways can you draw a...

College Algebra (MindTap Course List)

True or False? In Exercises 65-68, determine whether the statement is true or false. If it is false, explain wh...

Calculus (MindTap Course List)

Using the data of Exercise 16.13, estimate the mean difference in height velocity before and during growth horm...

Introduction To Statistics And Data Analysis

Automobile unit sales at B. J. Scott Motors, Inc., provided the following 10-year time series. Year Sales Year ...

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

True or False:
The function f is continuous at (0, 0), where

Study Guide for Stewart's Multivariable Calculus, 8th

If 13f(x)dx=10 and 13g(x)dx=6, then 13(2f(x)3g(x))dx= a) 2 b) 4 c) 18 d) 38

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

Information about mutual funds provided by Morningstar includes the type of mutual fund (Domestic Equity, Inter...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Define primary and secondary sources and explain how each plays a role in the process of finding a research ide...

Research Methods for the Behavioral Sciences (MindTap Course List)

Describe the general characteristics of the observational research design; explain its strengths and weaknesses...

Research Methods for the Behavioral Sciences (MindTap Course List)

Maximum Curvature In Exercises 49-54, (a) find the point on the curve at which the curvature is a maximum and (...

Multivariable Calculus

Let the universal set be R, the set of all real numbers, and let A={xR3x0},B={xR-x2} , and C={xR6x8}. Find each...

Discrete Mathematics With Applications

In Problems 39-44 proceed as in Examples 7 and 8 to find a solution of the given boundary-value problem. 40. y ...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Complete the chart in Figure 7.34. Do not round off the decimals in the third column. As you read down the thir...

Mathematics: A Practical Odyssey

Using Properties of Logarithms In Exercises 13-18, use the properties of logarithms to write the logarithm in t...

College Algebra

Consider the following hypothesis test:
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Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Round each percentage increase or decrease that you calculate to the nearest tenth of a percent. Function from ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

42. A Gallup Poll showed that 30% of Americans are satisfied with the way things are going in the United States...

Essentials Of Statistics For Business & Economics