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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 3.5, Problem 28ES

Textbook Problem

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Use the indicated letters to write the argument in symbolic form. Then use a truth table to determine whether the argument is valid or invalid.

If the winds are from the east (*e*), then we will not have a big surf (-s). We do not have a big surf. Therefore, the winds are from the east.

To determine

**To identify:**

The symbolic form of the given argument and check whether the given argument is valid or invalid using the truth table

**Given information:**

If the winds are from the east

**Concept Involved:**

__An Argument and a Valid Argument__: Anargumentconsists of a set of statements calledpremisesand another statement called theconclusion. An argument isvalidif the conclusion is true whenever all the premises are assumed to be true. An argument isinvalidif 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.

The following truth table procedure can be used to determine whether an argument is valid or invalid.

Truth Table Procedure to Determine the Validity of an Argument:

- Write the argument in symbolic form.
- Construct a truth table that shows the truth value of each premise and the truth value of the conclusion for all combinations of truth values of the simple statements.
- If the conclusion is true in every row of the truth table in which all the premises are true, the argument is valid. If the conclusion is false in any row in which all the premises are true, the argument is valid.

A conditional statement, symbolized by

**Calculation:**

In the argument given, the two premises and the conclusion are shown below. It is customary to place a horizontal line between the premises and the conclusion.

Representation of Argument | Symbolic form |

If the winds are from the east , then we will not have big surf We do not have big surf |

Mathematical Excursions (MindTap Course List)

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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. 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Understanding Basic Statistics

Fill in the missing entries in the product matrix. [312120132][132321210]=[477755]

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 516, evaluate the given quantity. log1/212

Finite Mathematics and Applied Calculus (MindTap Course List)

SOC The college administration is considering a total ban on student automobiles. You have conducted a poll on ...

Essentials Of Statistics

Find the scalar and vector projections of b onto a. 40. a = 1, 4, b = 2, 3

Multivariable Calculus

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Calculus: Early Transcendentals

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

Determine whether the following statement is true or false, if its false, explain why or give an example to sho...

Calculus: Early Transcendental Functions

Prove that limx21x=12.

Single Variable Calculus

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Calculus: An Applied Approach (MindTap Course List)

Annie and Alvie have agreed to meet between 5:00 p.m. and 6:00 p.m. for dinner at a local health-food restauran...

Probability and Statistics for Engineering and the Sciences

Stephens, Atkins, and Kingston (2009) conducted an experiment in which participants were able to tolerate more ...

Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 35-42, find functions f and g such that h = g f. (Note: The answer is not unique.) 40. h(x)=1x24

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

For Problems 55-94, simplify each numerical expression. Objectives 7 (7)(7)(6)(4)

Intermediate Algebra

Suppose that f has domain A and g has domain B. (a) What is the domain of f + g? (b) What is the domain of fg? ...

Single Variable Calculus: Early Transcendentals, Volume I

Factor each trinomial completely: a2+29a+100

Elementary Technical Mathematics

Three vertices of rectangle ABCD are A-5,1, B-2,-3, and C6,y. Find the value of y and also the fourth vertex.

Elementary Geometry For College Students, 7e

E-Z Kwik Grocery Store had cost of goods sold of $756,400 for the year. If the beginning inventory at cost was ...

Contemporary Mathematics for Business & Consumers

Find the magnitude of each of the following vectors. U=5i+12j

Trigonometry (MindTap Course List)

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Label each of the following statements as either true or false.
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Elements Of Modern Algebra

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Single Variable Calculus: Early Transcendentals

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Finite Mathematics for the Managerial, Life, and Social Sciences

Determine whether each triple (a,b,c) is a Pythagorean triple. a)(8,15,17)c)(6,8,10)b)(10,13,19)d)(11,17,20)

Elementary Geometry for College Students

Arc Length Consider the logarithmic spiral r=ea where a is a constant greater than 0 (see figure). Find the arc...

Calculus of a Single Variable

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Calculus: Early Transcendental Functions (MindTap Course List)

Express each area as indicated. Round each answer to the same number of significant digits as in the original q...

Mathematics For Machine Technology

Figure 3.51 gives the estimated number of diagnoses of AIDS in the United States by age at the time of diagnosi...

Mathematics: A Practical Odyssey

Product filling weights are normally distributed with a mean of 350 grams and a standard deviation of 15 grams....

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The graph of each function is a reflection of the graph of y=x2,y=x3,y=x,y=x,ory=x3.Graph each function. hx=-x3

College Algebra (MindTap Course List)

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

True or False:
If , then converge absolutely.

Study Guide for Stewart's Multivariable Calculus, 8th

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Introduction To Statistics And Data Analysis

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Calculus (MindTap Course List)

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Research Methods for the Behavioral Sciences (MindTap Course List)