Discrete Mathematics With Applications
5th Edition
ISBN: 9781337694193
Author: EPP, Susanna S.
Publisher: Cengage Learning,
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Textbook Question
Chapter 2.2, Problem 8TY
“R is a sufficient condition for S” means “if ______then_________”
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Students have asked these similar questions
Q7. A business office orders paper supplies from one of three vendors, V₁, V2, or V3.
Orders are to be placed on two successive days, one order per day. Thus, (V2, V3)
might denote that vendor V2 gets the order on the first day and vendor V3 gets the
order on the second day.
(a) List the sample points in this experiment of ordering paper on two successive
days.
(b) Assume the vendors are selected at random each day and assign a probability
to each sample point.
(c) Let A denote the event that the same vendor gets both orders and B the event
that V2 gets at least one order. Find P(A), P(B), P(AUB), and P(An B) by
summing the probabilities of the sample points in these events.
Question 1
-
Q5. Extend Theorem 5 (P(AUB) = P(A) + P(B) = P(ANB)), proved in class, to three
events, A, B and C, by finding an expression for P(AUBUC) in terms of the
probabilities of A, B and C, of their pair-wise intersections, and the intersection of
all three events. (Hint: Begin by considering AUB as a single event).
Chapter 2 Solutions
Discrete Mathematics With Applications
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. 31ESCh. 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. 5TYCh. 2.2 - A conditional statement and its contrapositive...Ch. 2.2 - Prob. 7TYCh. 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. 10TYCh. 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. 4ESCh. 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. 7ESCh. 2.2 - Prob. 8ESCh. 2.2 - Construct truth tables for the statements forms in...Ch. 2.2 - Prob. 10ESCh. 2.2 - Prob. 11ESCh. 2.2 - Use the logical equivalence established in Example...Ch. 2.2 - Prob. 13ESCh. 2.2 - Show that the following statement forms are all...Ch. 2.2 - Determine whether the following statement forms...Ch. 2.2 - Prob. 16ESCh. 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. 24ESCh. 2.2 - Prob. 25ESCh. 2.2 - Use truth tables to establish the truth of each...Ch. 2.2 - Prob. 27ESCh. 2.2 - Prob. 28ESCh. 2.2 - If statement forms P and Q are logically...Ch. 2.2 - Prob. 30ESCh. 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. 33ESCh. 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. 39ESCh. 2.2 - Prob. 40ESCh. 2.2 - Prob. 41ESCh. 2.2 - Prob. 42ESCh. 2.2 - Use the contrapositive to rewrite the statements...Ch. 2.2 - Prob. 44ESCh. 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. 3TYCh. 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. 7ESCh. 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. 14ESCh. 2.3 - Prob. 15ESCh. 2.3 - Prob. 16ESCh. 2.3 - Prob. 17ESCh. 2.3 - Use truth table to show that the argument forms...Ch. 2.3 - Prob. 19ESCh. 2.3 - Prob. 20ESCh. 2.3 - Prob. 21ESCh. 2.3 - Prob. 22ESCh. 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. 25ESCh. 2.3 - Some at the arguments in 24—32 are valid, whereas...Ch. 2.3 - Prob. 27ESCh. 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. 35ESCh. 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. 38ESCh. 2.3 - The famous detective Percule Hoirot was called in...Ch. 2.3 - Prob. 40ESCh. 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. 3TYCh. 2.4 - Prob. 4TYCh. 2.4 - Prob. 5TYCh. 2.4 - Prob. 6TYCh. 2.4 - Prob. 1ESCh. 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. 5ESCh. 2.4 - Prob. 6ESCh. 2.4 - Prob. 7ESCh. 2.4 - In 5-8, write an input/output table for the...Ch. 2.4 - Prob. 9ESCh. 2.4 - In 9-12, find the Boolean expression that...Ch. 2.4 - Prob. 11ESCh. 2.4 - In 9-12, find the Boolean expression that...Ch. 2.4 - Prob. 13ESCh. 2.4 - Construct circuits for the Boolean expressions in...Ch. 2.4 - Prob. 15ESCh. 2.4 - Prob. 16ESCh. 2.4 - Prob. 17ESCh. 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. 29ESCh. 2.4 - For the circuits corresponding to the Boolean...Ch. 2.4 - Prob. 31ESCh. 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. 2TYCh. 2.5 - Prob. 3TYCh. 2.5 - Prob. 4TYCh. 2.5 - Prob. 5TYCh. 2.5 - Prob. 6TYCh. 2.5 - Prob. 7TYCh. 2.5 - Prob. 8TYCh. 2.5 - Prob. 9TYCh. 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. 3ESCh. 2.5 - Prob. 4ESCh. 2.5 - Prob. 5ESCh. 2.5 - Prob. 6ESCh. 2.5 - Represent the integers in 7-12 in decimal...Ch. 2.5 - Prob. 8ESCh. 2.5 - Prob. 9ESCh. 2.5 - Represent the integers in 7—12 in decimal...Ch. 2.5 - Prob. 11ESCh. 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. 14ESCh. 2.5 - Prob. 15ESCh. 2.5 - Prob. 16ESCh. 2.5 - Prob. 17ESCh. 2.5 - Prob. 18ESCh. 2.5 - Prob. 19ESCh. 2.5 - Prob. 20ESCh. 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. 23ESCh. 2.5 - Prob. 24ESCh. 2.5 - Prob. 25ESCh. 2.5 - Prob. 26ESCh. 2.5 - Prob. 27ESCh. 2.5 - Prob. 28ESCh. 2.5 - Prob. 29ESCh. 2.5 - Prob. 30ESCh. 2.5 - Prob. 31ESCh. 2.5 - Prob. 32ESCh. 2.5 - Use 8-bit two’s complements to compute the surms...Ch. 2.5 - Prob. 34ESCh. 2.5 - Prob. 35ESCh. 2.5 - Prob. 36ESCh. 2.5 - Prob. 37ESCh. 2.5 - Prob. 38ESCh. 2.5 - Prob. 39ESCh. 2.5 - Convert the integers in 38-40 from hexadecimal to...Ch. 2.5 - Prob. 41ESCh. 2.5 - Prob. 42ESCh. 2.5 - Convert the integers in 41-43 from hexadecimal to...Ch. 2.5 - Prob. 44ESCh. 2.5 - Prob. 45ESCh. 2.5 - Prob. 46ESCh. 2.5 - Prob. 47ES
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