5th Edition

ISBN: 9780357097717

Author: EPP

Publisher: CENGAGE L

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Chapter 2.1, Problem 48ES

In 48 and 49 below, a logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step. ( p Λ ~ q ) ν ( p Λ q ) = p Λ ( Q q ν q ) by ( a ) = p Λ ( q ν ~ q ) by ( b ) = p Λ t by(c) = p by(d)

Therefore, ( p Λ ~ q ) ν ( p Λ q ) = p .

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Chapter 2 Solutions

DISCRETE MATHEMATICS WITH APPLICATION (

Ch. 2.1 - An and statement is true when, and only when, both...Ch. 2.1 - An or statement is false when, and only when, both...Ch. 2.1 - Two statement forms are logically equivalent when,...Ch. 2.1 - De Morgan’s laws say (1) that the negation of an...Ch. 2.1 - A tautology is a statement that is always _____.Ch. 2.1 - A contradiction is a statement that is always...Ch. 2.1 - In eachof 1—4 represent the common form of each...Ch. 2.1 - In each of 1-4 represent the common form of each...Ch. 2.1 - In each of 1—4 represent the common form of each...Ch. 2.1 - In each of 1—4 represent the common form of each...

Ch. 2.1 - Indicate which of the following sentences are...Ch. 2.1 - Write the statements in 6-9 in symbolic form using...Ch. 2.1 - Write the statements in 6-9 in symbolic form using...Ch. 2.1 - Write the statements in 6-9 n symbolic form using...Ch. 2.1 - Write the statements in 6-9 in symbolic form using...Ch. 2.1 - Let p be the statement "DATAENDFLAG is off," q the...Ch. 2.1 - In the following sentence, is the word or used in...Ch. 2.1 - Write truth tables for the statement forms in...Ch. 2.1 - Write truth tables for the statement forms in...Ch. 2.1 - Write truth tables for the statement forms in...Ch. 2.1 - Write truth tables for the statement forms in...Ch. 2.1 - Determine whether the statement forms in 16—24 are...Ch. 2.1 - Determine whether the statement forms in 16-24 are...Ch. 2.1 - Determine whether the statement forms in 16—24 are...Ch. 2.1 - Determine whether the statement forms in 16—24 are...Ch. 2.1 - Determine whether the statement forms in 16—24 are...Ch. 2.1 - Determine whether the statement forms in 16-24 are...Ch. 2.1 - Determine whether the statement forms in 16-24 are...Ch. 2.1 - Determine whether the statement forms in 16-24 are...Ch. 2.1 - Determine whether the statement forms in 16-24 are...Ch. 2.1 - Use De Morgan’s laws to write negations for the...Ch. 2.1 - Use De Morgan’s laws to write negations for the...Ch. 2.1 - Use De Morgan’s laws to write negations for the...Ch. 2.1 - Use De Morgan’s laws to write negations for the...Ch. 2.1 - Use De Morgan’s laws to write negations for the...Ch. 2.1 - Use De Morgan’s laws to write negations for the...Ch. 2.1 - Prob. 31ES Ch. 2.1 - Assume x is a particular real number and use De...Ch. 2.1 - Assume x is a particular real number and use De...Ch. 2.1 - Assume x is a particular real number and use De...Ch. 2.1 - Assume x is a particular real number and use De...Ch. 2.1 - Assume x is a particular real number and use De...Ch. 2.1 - Assume x is a particular real number and use De...Ch. 2.1 - In 38 and 39, imagine that num_orders and...Ch. 2.1 - In 38 and 39, imagine that num_orders and...Ch. 2.1 - Use truth to establish which of the statement...Ch. 2.1 - Use truth tables to establish which of the...Ch. 2.1 - Use truth to establish which of the statement...Ch. 2.1 - Use truth tables to establish which of the...Ch. 2.1 - Recall that axb means that ax and xb . Also ab...Ch. 2.1 - Determine whether the statements in (a) and (b)...Ch. 2.1 - Let the symbol denote exclusive or; so...Ch. 2.1 - In logic and in standard English, a double...Ch. 2.1 - In 48 and 49 below, a logical equivalence is...Ch. 2.1 - In 48 and 49 below, a logical equivalence is...Ch. 2.1 - Use Theorem 2.11 to verify the logical...Ch. 2.1 - Use theorem 2.11 to verify the logical...Ch. 2.1 - Use Theorem 2.11 to verify the logical...Ch. 2.1 - Use Theorem 2.11 to verify the logical...Ch. 2.1 - Use Theorem 2.11 to verify the logical...Ch. 2.2 - An if-then statement is false if, and only if, the...Ch. 2.2 - The negation of “if p then q” is _____Ch. 2.2 - The converse of”if p then q” is _______Ch. 2.2 - The contrapositive of “if p the q” is _________Ch. 2.2 - Prob. 5TY Ch. 2.2 - A conditional statement and its contrapositive...Ch. 2.2 - Prob. 7TY Ch. 2.2 - “R is a sufficient condition for S” means “if...Ch. 2.2 - “R is a necessary condition for S” means “if...Ch. 2.2 - Prob. 10TY Ch. 2.2 - Rewrite the statements in 1-4 in if-then form.Ch. 2.2 - Rewrite the statements in 1-4 in if-then from. I...Ch. 2.2 - Rewrite the statements in 1-4 in if-then form....Ch. 2.2 - Prob. 4ES Ch. 2.2 - Construct truth tables for the statements forms in...Ch. 2.2 - Construct truth tables for the statements forms in...Ch. 2.2 - Prob. 7ES Ch. 2.2 - Prob. 8ES Ch. 2.2 - Construct truth tables for the statements forms in...Ch. 2.2 - Prob. 10ES Ch. 2.2 - Prob. 11ES Ch. 2.2 - Use the logical equivalence established in Example...Ch. 2.2 - Prob. 13ES Ch. 2.2 - Show that the following statement forms are all...Ch. 2.2 - Determine whether the following statement forms...Ch. 2.2 - Prob. 16ES Ch. 2.2 - In 16 and 17, write each o the two statements in...Ch. 2.2 - Write each at the following three statements in...Ch. 2.2 - True or false? The negation of “If Sue is Luiz’s...Ch. 2.2 - Write negations for each of the following...Ch. 2.2 - Suppose that p and q are statements so that p ) q...Ch. 2.2 - Write negations for each of the following...Ch. 2.2 - Write negations for each of the following...Ch. 2.2 - Prob. 24ES Ch. 2.2 - Prob. 25ES Ch. 2.2 - Use truth tables to establish the truth of each...Ch. 2.2 - Prob. 27ES Ch. 2.2 - Prob. 28ES Ch. 2.2 - If statement forms P and Q are logically...Ch. 2.2 - Prob. 30ES Ch. 2.2 - If statement forms P mid Q are logically...Ch. 2.2 - Rewrite each of the statements in 32 and 33 as a...Ch. 2.2 - Prob. 33ES Ch. 2.2 - Rewrite the statements in 34 and 35 in if-then...Ch. 2.2 - Rewrite the statements in 34 and 35 en in-then...Ch. 2.2 - Taking the long view on u education, you go to the...Ch. 2.2 - Some prograrnming languages use statements of the...Ch. 2.2 - Some programming languages use statements of the...Ch. 2.2 - Prob. 39ES Ch. 2.2 - Prob. 40ES Ch. 2.2 - Prob. 41ES Ch. 2.2 - Prob. 42ES Ch. 2.2 - Use the contrapositive to rewrite the statements...Ch. 2.2 - Prob. 44ES Ch. 2.2 - Note that a sufficient condition lot s is r”...Ch. 2.2 - “If compound X is boiling, then its temperature...Ch. 2.2 - In 47— 50(a)use the logical equivalences pq=~pq...Ch. 2.2 - In 47— 50(a)use the logical equivalences pq=~pq...Ch. 2.2 - In 47-50 (a) use the logical equivalences pq=~pq...Ch. 2.2 - In 47-50(a) use the logical equivalences pq=~pq...Ch. 2.2 - Given any statement form, is it possible to find a...Ch. 2.3 - For an argument to be valid means that every...Ch. 2.3 - For an argument to be invalid means that there is...Ch. 2.3 - Prob. 3TY Ch. 2.3 - Use modus ponens at modus tollens to fill in the...Ch. 2.3 - Use modus ponens or modus tollens to fill in the...Ch. 2.3 - Use modus ponens or modus tollens to fill in the...Ch. 2.3 - Use modus ponens at modus tollens to fill in the...Ch. 2.3 - Use modus ponens or modus tollens to fill in the...Ch. 2.3 - Use truth tables to determine whether the argument...Ch. 2.3 - Prob. 7ES Ch. 2.3 - Use truth tables to determine whether the argument...Ch. 2.3 - Use truth tables to determine whether the argument...Ch. 2.3 - Use truth tables to determine whether the argument...Ch. 2.3 - Use truth tables to determine whether the argument...Ch. 2.3 - Use truth table to show that the following forms...Ch. 2.3 - Use truth tables to show that the argument forms...Ch. 2.3 - Prob. 14ES Ch. 2.3 - Prob. 15ES Ch. 2.3 - Prob. 16ES Ch. 2.3 - Prob. 17ES Ch. 2.3 - Use truth table to show that the argument forms...Ch. 2.3 - Prob. 19ES Ch. 2.3 - Prob. 20ES Ch. 2.3 - Prob. 21ES Ch. 2.3 - Prob. 22ES Ch. 2.3 - Use symbols to write the logical form of each...Ch. 2.3 - Some of the argurnents in 24-32 are valid, whereas...Ch. 2.3 - Prob. 25ES Ch. 2.3 - Some at the arguments in 24—32 are valid, whereas...Ch. 2.3 - Prob. 27ES Ch. 2.3 - Some of the argents in 24-32 are valid. wherere as...Ch. 2.3 - Some of the arguments in 24-32 are valid, whereas...Ch. 2.3 - Some of the arguments in 24-32 are valid, whereas...Ch. 2.3 - Some of the arguments in 24-32 are valis, whereas...Ch. 2.3 - Some of the arguments in 24-32 are valid, whereas...Ch. 2.3 - Give an example (other then Example 2.3.11) of a...Ch. 2.3 - Give an example (other than Example 2.3.12) of an...Ch. 2.3 - Prob. 35ES Ch. 2.3 - Given the following information about a computer...Ch. 2.3 - In the back of an old cupboard you discusser a...Ch. 2.3 - Prob. 38ES Ch. 2.3 - The famous detective Percule Hoirot was called in...Ch. 2.3 - Prob. 40ES Ch. 2.3 - In 41—44 a set a pren.sei and a conclusion arc...Ch. 2.3 - In 41-44 a set premises and a conclusion are...Ch. 2.3 - In 41-44 a set premises and a conclusion are...Ch. 2.3 - In 41-44 a wt o premises and a conclusion are...Ch. 2.4 - The input/output table for a digital logic circuit...Ch. 2.4 - The Boolean expression that corresponds to a...Ch. 2.4 - Prob. 3TY Ch. 2.4 - Prob. 4TY Ch. 2.4 - Prob. 5TY Ch. 2.4 - Prob. 6TY Ch. 2.4 - Prob. 1ES Ch. 2.4 - Give the output signals for the circuits in 1—4 if...Ch. 2.4 - Give the output signals for the circuits in 1—4 if...Ch. 2.4 - Give the output signals for the circuits in 1-4 if...Ch. 2.4 - Prob. 5ES Ch. 2.4 - Prob. 6ES Ch. 2.4 - Prob. 7ES Ch. 2.4 - In 5-8, write an input/output table for the...Ch. 2.4 - Prob. 9ES Ch. 2.4 - In 9-12, find the Boolean expression that...Ch. 2.4 - Prob. 11ES Ch. 2.4 - In 9-12, find the Boolean expression that...Ch. 2.4 - Prob. 13ES Ch. 2.4 - Construct circuits for the Boolean expressions in...Ch. 2.4 - Prob. 15ES Ch. 2.4 - Prob. 16ES Ch. 2.4 - Prob. 17ES Ch. 2.4 - For each of the tables in 18-21, construct (a) a...Ch. 2.4 - For each of the tables in 18-21, construct (a) a...Ch. 2.4 - For each of the tables in 18-21, construct (a) a...Ch. 2.4 - For each of the tables in 18-21, construct (a) a...Ch. 2.4 - Design a circuit to take input signals P,Q, and R...Ch. 2.4 - Design a circuit to take input signals P,Q, and R...Ch. 2.4 - The light in a classroom are controlled by two...Ch. 2.4 - An alarm system has three different control panels...Ch. 2.4 - Use the properties listed in Thearem 2.1.1 to to...Ch. 2.4 - Use the properties listed in Theorem 2.1.1 to show...Ch. 2.4 - Use the properties kited in Theorem 2.1.1 to show...Ch. 2.4 - Prob. 29ES Ch. 2.4 - For the circuits corresponding to the Boolean...Ch. 2.4 - Prob. 31ES Ch. 2.4 - The Boolean expression for the circuit in Example...Ch. 2.4 - Show that for the Sheffer stroke |, PQ(PQ)(PQ)....Ch. 2.4 - Show that the following logical equivalences hold...Ch. 2.5 - To represent a nonnegative integer in binary...Ch. 2.5 - Prob. 2TY Ch. 2.5 - Prob. 3TY Ch. 2.5 - Prob. 4TY Ch. 2.5 - Prob. 5TY Ch. 2.5 - Prob. 6TY Ch. 2.5 - Prob. 7TY Ch. 2.5 - Prob. 8TY Ch. 2.5 - Prob. 9TY Ch. 2.5 - Represent the decimal integers in 1-6 in binary...Ch. 2.5 - Represent the decimal integers in 1-6 in binary...Ch. 2.5 - Prob. 3ES Ch. 2.5 - Prob. 4ES Ch. 2.5 - Prob. 5ES Ch. 2.5 - Prob. 6ES Ch. 2.5 - Represent the integers in 7-12 in decimal...Ch. 2.5 - Prob. 8ES Ch. 2.5 - Prob. 9ES Ch. 2.5 - Represent the integers in 7—12 in decimal...Ch. 2.5 - Prob. 11ES Ch. 2.5 - Represent the integers in 7—12 in decimal...Ch. 2.5 - Perform the arithmetic in 13-20 using binary...Ch. 2.5 - Prob. 14ES Ch. 2.5 - Prob. 15ES Ch. 2.5 - Prob. 16ES Ch. 2.5 - Prob. 17ES Ch. 2.5 - Prob. 18ES Ch. 2.5 - Prob. 19ES Ch. 2.5 - Prob. 20ES Ch. 2.5 - Give the output singals S and T for the circuit...Ch. 2.5 - Add 111111112+12 and convert the result to decimal...Ch. 2.5 - Prob. 23ES Ch. 2.5 - Prob. 24ES Ch. 2.5 - Prob. 25ES Ch. 2.5 - Prob. 26ES Ch. 2.5 - Prob. 27ES Ch. 2.5 - Prob. 28ES Ch. 2.5 - Prob. 29ES Ch. 2.5 - Prob. 30ES Ch. 2.5 - Prob. 31ES Ch. 2.5 - Prob. 32ES Ch. 2.5 - Use 8-bit two’s complements to compute the surms...Ch. 2.5 - Prob. 34ES Ch. 2.5 - Prob. 35ES Ch. 2.5 - Prob. 36ES Ch. 2.5 - Prob. 37ES Ch. 2.5 - Prob. 38ES Ch. 2.5 - Prob. 39ES Ch. 2.5 - Convert the integers in 38-40 from hexadecimal to...Ch. 2.5 - Prob. 41ES Ch. 2.5 - Prob. 42ES Ch. 2.5 - Convert the integers in 41-43 from hexadecimal to...Ch. 2.5 - Prob. 44ES Ch. 2.5 - Prob. 45ES Ch. 2.5 - Prob. 46ES Ch. 2.5 - Prob. 47ES

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In 48 and 49 below, a logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step. ( p Λ ~ q ) ν ( p Λ q ) = p Λ ( Q q ν q ) by ( a ) = p Λ ( q ν ~ q ) by ( b ) = p Λ t by(c) = p by(d) Therefore, ( p Λ ~ q ) ν ( p Λ q ) = p .

Solution Summary: The author explains the logical equivalence derived from the theorem 2.1.1 for pwedge (qvee r)=p

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Chapter 2 Solutions