DISCRETE MATHEMATICS WITH APPLICATION (

5th Edition

ISBN: 9780357097717

Author: EPP

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Statements and Logic

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

Videos

Textbook Question

Chapter 2.4, Problem 34ES

Show that the following logical equivalences hold for the Peirce arrow ↓ , where P ↓ Q = ~ ( P ν Q )

~ P = P ↓ P

P ν Q = ( P ↓ Q ) ↓ ( P ↓ Q )

P Λ Q = ( P ↓ P ) ↓ ( Q ↓ Q )

Write P → Q

using Peirce arrows only.

Write P ↔ Q

using Peirce arrows only.

Expert Solution & Answer

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

Show that the following logical equivalences hold for the Peirce arrow ↓ , where P ↓ Q = ~ ( P ν Q ) ~ P = P ↓ P P ν Q = ( P ↓ Q ) ↓ ( P ↓ Q ) P Λ Q = ( P ↓ P ) ↓ ( Q ↓ Q ) Write P → Q using Peirce arrows only. Write P ↔ Q using Peirce arrows only.

Solution Summary: The author explains that the logical equivalence holds true for pierce arrows.

Concept explainers

Videos

Chapter 2 Solutions