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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 3.3, Problem 19ES
Textbook Problem
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Construct a truth table for the given Statement.

[ r ( p q ) ] ( r q )

To determine

To construct a truth table for the given statement.

Explanation of Solution

Given information:

Given statement is [r(~pq)](r ~q)

Calculation:

The standard truth table for two statements is given by,

  p  q  r
TTT
TTF
TFT
TFF
FTT
FTF
FFT
FFF

Then the negations are calculated,

  p  q  r  ~p  ~q
TTTFF
TTFFF
TFTFT
TFFFT
FTTTF
FTFTF
FFTTT
FFFTT

Now the statement (~p q) is calculated. The statement contains 'or', so the statement will be false when both the statements are false. Else the statement will always be true.

  p  q  r  ~p  ~q  (~p q)
TTTFFT
TTFFFT
TFTFTF
TFFFTF
FTTTFT
FTFTFT
FFTTTT
FFFTTT

Now the statement [r(~p q)] is calculated. The statement contains 'and', so the statement will be true when both the statements are true. Else the statement will always be false.

  p  q  r  ~p  ~q  (~p q)  [r(~p q)]
TTTFFTT
TTFFFTF
TFTFTFF
TFFFTFF
FTTTFTT
FTFTFTF
FFTTTTT
FFFTTTF

Now the statement (r ~q) is calculated. The statement contains 'or', so the statement will be false when both the statements are false. Else the statement will always be true

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Chapter 3 Solutions

Mathematical Excursions (MindTap Course List)
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Ch. 3.1 - Draw a network to represent each statement. [ PQR...Ch. 3.1 - Draw a network to represent each statement....Ch. 3.1 - Draw a network to represent each statement. [...Ch. 3.1 - Draw a network to represent each statement....Ch. 3.1 - Warning Circuits The circuits shown in Excursion...Ch. 3.1 - Warning Circuits The circuits shown in Excursion...Ch. 3.1 - Determine whether each sentence is a statement....Ch. 3.1 - Determine whether each sentence is a statement....Ch. 3.1 - Determine whether each sentence is a statement....Ch. 3.1 - Determine whether each sentence is a statement....Ch. 3.1 - Determine whether each sentence is a statement....Ch. 3.1 - Determine whether each sentence is a statement. 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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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In problems 23-58, perform the indicated operations and simplify. 30.

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Let f(x) = {x21if2x1x3if1x2 Find (a) limx1 f(x) and limx1+ f(x). Is f continuous at x = 1? Explain.

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Evaluate limx1x31x1.

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What are the two requirements for a random sample?

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Expand each expression in Exercises 122. (x2+x1)(2x+4)

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Prove each identity. cos(A+B)sinAcosB=cotAtanB

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Find x so that -2,3, x,6, and 8,8 are collinear.

Elementary Geometry for College Students

(k=mnak)(k=mnbk)=

Discrete Mathematics With Applications

Sometimes, Always, or Never: dx equals the area between y = f(x), the x-axis, x = a, and x = b.

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

The equation of the line through (4, 10, 8) and (3, 5, 1) is:

Study Guide for Stewart's Multivariable Calculus, 8th

3.4 SKILL BUILDING EXERCISES Correlation Coefficient The correlation coefficient r is a measure of how well a r...

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Explain the purpose of a research proposal and how it differs from a research report.

Research Methods for the Behavioral Sciences (MindTap Course List)

Suppose N = 15 and r = 4. What is the probability of x = 3 for n = 10?

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