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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 3.4, Problem 15ES

Textbook Problem

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

Every parallelogram is a quadrilateral.

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

(a) Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the point (/6, 1). ...

Multivariable Calculus

The following exercise are intended only for these who have already covered Chapter 6. Evaluate the integral. 0...

Calculus (MindTap Course List)

Shrinkage in Concrete Beams As concrete dries, it shrinksthe higher the water content, the greater the shrinkag...

Precalculus: Mathematics for Calculus (Standalone Book)

Determining Continuity In Exercises 11-40, describe the interval(s) on which the function is continuous. Explai...

Calculus: An Applied Approach (MindTap Course List)

At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in2. Bel...

Calculus: Early Transcendentals

For Problems 79-99, answer the question with an algebraic expression. Objective 3 The perimeter of a square is ...

Intermediate Algebra

Evaluate the difference quotient for the given function. Simplify your answer. 29. f(x)=1x,f(x)f(a)xa

Single Variable Calculus

For the following sample of n = 10 scores: a. Assume that the scores are measurements of a discrete variable an...

Statistics for The Behavioral Sciences (MindTap Course List)

The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be reg...

Probability and Statistics for Engineering and the Sciences

Modeling Data The average typing speeds S (in words per minute) of a typing student after t weeks of lessons ar...

Calculus: Early Transcendental Functions

Let a=log2,b=log3, and c=log7. In Exercises 2946, use the logarithm identities to express the given quantity in...

Applied Calculus

Production Costs When Duffin House printed a million copies of Larry Plotter and the Simplex Method (see Exerci...

Finite Mathematics and Applied Calculus (MindTap Course List)

Statistical Literacy Random sample of size 9 is taken from a normal distribution with mean 10 and standard devi...

Understanding Basic Statistics

SOC/CJ Statewide, the police clear by arrest 35 of the robberies and 42 of the aggravated assaults reported to ...

Essentials Of Statistics

Evaluate the definite integral. 01xex2dx

Single Variable Calculus: Early Transcendentals, Volume I

Add: (6)+(+9)

Elementary Technical Mathematics

For the right triangle shown, express each ratio as a fraction in lowest terms: a cos b sin

Elementary Geometry For College Students, 7e

Consider the additive group of real numbers. Prove or disprove that each of the following mappings : is an iso...

Elements Of Modern Algebra

Solve for if 0360. sin3cos=3

Trigonometry (MindTap Course List)

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of...

Single Variable Calculus: Early Transcendentals

Use the ordinary interest method to compute the time for the following loans. Round answers to the next higher ...

Contemporary Mathematics for Business & Consumers

VOTING QUORUMS A quorum minimum of 6 voting members is required at all meetings of the Curtis Townhomes Owners ...

Finite Mathematics for the Managerial, Life, and Social Sciences

Given that x is the measure of an angle, name the type of angle when: a x=90__________ b 90x180______

Elementary Geometry for College Students

Finding a Derivative In Exercises 29-40, Find the derivative of the algebraic function. f(x)=21xx3

Calculus of a Single Variable

Finding an Inverse Function In Exercises 39-44, (a) find the inverse function or f, (b) use a graphing utility ...

Calculus: Early Transcendental Functions (MindTap Course List)

Program the hole locations of the following part drawings. The location dimensions given in the tables are take...

Mathematics For Machine Technology

A manufacturer of clay roofing tiles would like to investigate the effect of clay type on the proportion of til...

Introduction To Statistics And Data Analysis

ProofIn Exercises 6168, prove the property. In each case, assume r, u, and v are differentiable vector-valued f...

Multivariable Calculus

Applying the First Derivative Test In Exercises 19-40, (a) find the critical numbers of f, if any, (b) find the...

Calculus (MindTap Course List)

limnn2+3n2n2+n+1= a) 0 b) 12 c) 1 d)

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

For the vector function r(t) with unit tangent T, the principal unit normal vector is:

Study Guide for Stewart's Multivariable Calculus, 8th

Suppose a researcher conducts a two-factor study comparing two treatments (I and II) for college graduates vers...

Research Methods for the Behavioral Sciences (MindTap Course List)

Getting Ready You should be able to complete these vocabulary and concept statements before you proceed to the ...

College Algebra (MindTap Course List)

Describe the four probability sampling methods presented in the book, other than simple random sampling (strati...

Research Methods for the Behavioral Sciences (MindTap Course List)

Forty-minute workouts of one of the following activities three days a week will lead to a loss of weight. The f...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Net assets for the 50 largest stock mutual funds show a median of 15 billion. A sample of 10 of the 50 largest ...

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

Seven Lundgren buys a three-year-old Chevrolet from Skunk Motors for 14,600. He puts 300 down and finances the ...

Mathematics: A Practical Odyssey

An alternative proof of the irrationality of 2 counts the number of 2’s on the two sides of the equation 2n2=m2...

Discrete Mathematics With Applications

Raindrops Keep Falling ... When a bottle of liquid refreshment was opened recently, the following factoid was f...

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

Quartic Regression In Exercise S-8 through S-14, use regression to find a quartic model for the given data set....

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

13. Refer to the KALI problem presented in this section. The quality control manager requested a producer’s ris...

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

Potato Chip Quality Control. NDC Technology’s MM710e On-Line Snacks Gauge rapidly measures surface brownness of...

Essentials Of Statistics For Business & Economics