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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 3.4, Problem 21ES

Textbook Problem

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Write the a. converse, b. inverse, and c. contrapositive of the given statement.

She will visit Kauai only if she can extend her vacation for at least two days.

To determine

**(a)**

**To write:**

converse of the given statement

**Given information:**

The statement:

**Concept Involved:**

A statement that can be written in if-then form is called Conditional Statement. The phrase immediately following the word if is the hypothesis. The phrase immediately following the word then is the conclusion.

A Conditional Statement can be represented in symbols as

Statements that have the same truth values are logically equivalent. They are either both TRUE or both FALSE.

If you change the hypothesis or conclusion of a conditional statement, you form related conditionals. The below chart shows the three related conditionals, converse, inverse and contrapositive, and how they are related to a conditional statement

Logic | Symbols | Formed by |

Conditional | Using the given hypothesis and conclusion | |

Converse | Exchanging the hypothesis and conclusion | |

Inverse | Replacing the hypothesis with its negation and replacing the conclusion with its negation | |

Contrapositive | Negating the hypothesis, negating the conclusion, and switching them |

A conditional statement is logically equivalent to its contrapositive.

A conditional statement and its converse are NOT logically equivalent.

A conditional statement and its inverse are NOT logically equivalent.

The converse and the inverse of a conditional statement are logically equivalent to each other.

**Calculation:**

The statement can be rewritten as

To determine

**(b)**

**To write:**

inverse of the given statement

To determine

**(c)**

**To write:**

contrapositive of the given statement

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 - Use the indicated letters to write the argument in...Ch. 3.5 - Use the indicated letters to write the argument in...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Determine whether the argument is valid or invalid...Ch. 3.5 - Use a sequence of valid arguments to show that...Ch. 3.5 - Use a sequence of valid arguments to show that...Ch. 3.5 - Use a sequence of valid arguments to show that...Ch. 3.5 - Use a sequence of valid arguments to show that...Ch. 3.5 - Use a sequence of valid arguments to show that...Ch. 3.5 - 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Assume that no...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use an Euler diagram to determine whether the...Ch. 3.6 - Use all of the premises in each argument to...Ch. 3.6 - Use all of the premises in each argument to...Ch. 3.6 - Use all of the premises in each argument to...Ch. 3.6 - Use all of the premises in each argument to...Ch. 3.6 - Use all of the premises in each argument to...Ch. 3.6 - Use all of the premises in each argument to...Ch. 3.6 - Examine the following three premises: 1. 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Represent...Ch. 3 - Write the negation of each quantified statement....Ch. 3 - Write the negation of each quantified statement....Ch. 3 - Write the negation of each quantified statement....Ch. 3 - Write the negation of each quantified statement....Ch. 3 - Write the negation of each quantified statement....Ch. 3 - Write the negation of each quantified statement....Ch. 3 - Determine whether each statement is true or false....Ch. 3 - Determine whether each statement is true or false....Ch. 3 - Determine whether each statement is true or false....Ch. 3 - Determine whether each statement is true or false....Ch. 3 - Determine the truth value of the statement given...Ch. 3 - Determine the truth value of the statement given...Ch. 3 - Determine the truth value of the statement given...Ch. 3 - Determine the truth value of the statement given...Ch. 3 - Determine the truth value of the statement given...Ch. 3 - Determine the truth value of the statement given...Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Construct a truth table for the given statement....Ch. 3 - Construct a truth table for the given statement. [...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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Calculus: An Applied Approach (MindTap Course List)

Identifying a Conic An equation of a conic is given. (a) Use the discriminant to determine whether the graph of...

Precalculus: Mathematics for Calculus (Standalone Book)

Masculine-themed words (such us competitive, independent, analyze, strong) are commonly used in job recruitment...

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

a If F(x)=5x/(1+x2), find F(2) and use it to find an equation of the tangent line to the curve y=5x/(1+x2) at t...

Calculus (MindTap Course List)

In Exercises 516, evaluate the given quantity. log5125

Finite Mathematics and Applied Calculus (MindTap Course List)

Consider numerical observations x1,...,xn. It is frequently of interest to know whether the xi s are (at least ...

Probability and Statistics for Engineering and the Sciences

For problems 15-26, simplify each numerical expression. Be sure to take advantage of the properties whenever th...

Intermediate Algebra

In Exercises 2340, find the indicated limit. 29. limt1(2x33x2+x+2)

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

a. For each situation, find Zcritical. Alpha Form of the Test Zcritical 0.05 One-tailed 0.10 Two-tailed 0.06 T...

Essentials Of Statistics

Find the area of the surface. 39. The part of the plane 3x +2y+ z = 6 that lies in the first octant

Multivariable Calculus

The three cases in the First Derivative Test cover the situations one commonly encounters but do not exhaust al...

Single Variable Calculus: Early Transcendentals, Volume I

The Hill of Tara is located in south-central Meath, not far from Dublin. Ireland. Tara is of great cultural and...

Understanding Basic Statistics

A small-appliance manufacturer finds that it costs 9000 to produce 1000 toaster ovens a week and 12,000 to prod...

Single Variable Calculus

If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli'...

Calculus: Early Transcendentals

Jumbo shrimp are those that require 1015 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1...

Statistics for The Behavioral Sciences (MindTap Course List)

Finding Magnitudes In Exercises 39-42, find the following. u v u+v |uu vv u+vu+v u=2,4,v=5,5

Calculus: Early Transcendental Functions

Find the length of refer AC in Illustration 3. ILLUSTRATION 3

Elementary Technical Mathematics

Problems 1 through 10 refer to triangle ABC, which is not necessarily a right triangle. Use the Jaw of sines to...

Trigonometry (MindTap Course List)

Label each of the following statement as either true or false. 9. If ab and ba then a=b.

Elements Of Modern Algebra

Suppose that F, G, and Q are polynomials and F(x)Q(x)=G(x)Q(x) for all x except when Q(x) = 0. Prove that F(x) ...

Single Variable Calculus: Early Transcendentals

Complete Exercises 25-30 as they relate to the units-of-production method of depreciation. Round to the nearest...

Contemporary Mathematics for Business & Consumers

In Exercises 25 to 36, give the indirect proof for each problem or statement. In a plane, if two lines are inte...

Elementary Geometry For College Students, 7e

In Exercises 918, indicate whether the matrix is in row-reduced form. [1100|30]

Finite Mathematics for the Managerial, Life, and Social Sciences

Continuity of a Vector-Valued Function In Exercises 71-76, determine the interval(s) on which the vector-valued...

Calculus: Early Transcendental Functions (MindTap Course List)

For Exercises 39 to 40, use intuition to from a proportion based on the drawing shown. ABC has an inscribed rho...

Elementary Geometry for College Students

Coterminal Angles in Degrees In Exercises 5 and 6, determine two coterminal angles in degree measure (one posit...

Calculus of a Single Variable

Find each percentage. Round the answers to 2 decimal places when necessary. 16. 122% of 1.68

Mathematics For Machine Technology

Define counterbalancing and explain how it is used to minimize or eliminate threats to internal validity from t...

Research Methods for the Behavioral Sciences (MindTap Course List)

In mid-2016 the United Kingdom (UK) withdrew from the European Union (an event known as Brexit), causing econom...

Introduction To Statistics And Data Analysis

Differential Equation In Exercises 65-68, find the general solution of the differential equation using any meth...

Calculus (MindTap Course List)

Polar coordinates of the point with rectangular coordinates (5, 5) are:
(25, 0)

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

A hypothesis test attempts to rule out chance, or sampling error, as a plausible explanation for the results fr...

Research Methods for the Behavioral Sciences (MindTap Course List)

Bara Research Group conducted a survey about church attendance. The survey respondents were asked about their c...

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

True or False:
is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

Use a graphing calculator to evaluate each determinant. 2.35.76.13.46.28.35.88.29.2

College Algebra (MindTap Course List)

Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give the or...

Multivariable Calculus

Given that z is a standard normal random variable, find z for each situation. a. The area to the right of z is ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Consider a weighted die-one that has a small weight in its interior. Such a weight would cause the face closest...

Mathematics: A Practical Odyssey

A fair coin is tossed until either a head comes up or four tails are obtained. What is the expected number of t...

Discrete Mathematics With Applications

In Problems 118 use Definition 7.1.1 to find f(t). 4. f(t)={2t+1,0t10,t1

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

Marathon Runner Ages. The Flying Pig is a marathon (26.2 mile long) running race held every year in Cincinnati,...

Essentials Of Statistics For Business & Economics

Finding the Inverse of a Matrix: In Exercises 13-24, find the inverse of the matrix, if possible. 2153

College Algebra

Managers of 1200 different retail outlets make twice-a-month restocking orders from a central warehouse. Past e...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Parenthesis and Grouping 7.3-6.82.5+1.8

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