PROB SOLV APPROACH FOR TEACHERS MYLAB
12th Edition
ISBN: 9780137657988
Author: BILLSTEIN
Publisher: INTER PEAR
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Textbook Question
Chapter 2.3B, Problem 13A
The equation
a. Discover an equation involving
b. Verify the equation in a. for specific sets.
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k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
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1
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where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
4.
5.
6.
Prove that p (gp) is a tautology using the laws of propositional logic.
Prove that p((pVq) → q) is a tautology using the laws of propositional logic.
Let us say a natural number n is ok if there are two natural numbers whose sum
is n and whose product is n. (Convention: the natural numbers consist of 0, 1, 2,...)
(a) Give a logical expression that means "n is ok".
(b) Show that 0 and 4 are both ok.
(c) Give a logical expression that means "every natural number is ok".
(d) Give a logical expression that means "it is not the case that every number is ok". Push
the negations into the expression as far as possible.
7.
Let E(x, y) be a two-variable predicate meaning "x likes to eat y", where the
domain of x is people and the domain of y is foods. Write logical expressions that represent
the following English propositions:
(a) Alice doesn't like to eat pizza.
(b) Everybody likes to eat at least one food.
(c) Every student likes to eat at least one food other than pizza.
(d) Everyone other than Alice likes to eat at least two different foods.
(e) There are two different people that like to eat the same food.
Chapter 2 Solutions
PROB SOLV APPROACH FOR TEACHERS MYLAB
Ch. 2.1 - Explain why commands and questions are not...Ch. 2.1 - Explain how to write the negation of a quantified...Ch. 2.1 - a. Describe under what conditions a disjunction is...Ch. 2.1 - Consider the nursery rhyme. For want of a nail,...Ch. 2.1 - In an email address line, a coma or a semicolon is...Ch. 2.1 - If a statement and its converse are both true,...Ch. 2.1 - Table 5 shows a situation used to motivate the...Ch. 2.1 - A student in a logic class suggested that one...Ch. 2.1 - Discuss the paradox arising from the following set...Ch. 2.1 - Prob. 10MC
Ch. 2.1 - Write an explanation for a seventh grader showing...Ch. 2.1 - Prob. 12MCCh. 2.1A - Determine which of the following are statements...Ch. 2.1A - Use quantifiers to make each of the following...Ch. 2.1A - Use quantifiers to make each of equation in...Ch. 2.1A - Write the negation of each of the following...Ch. 2.1A - Identify the following as true or false. a. For...Ch. 2.1A - Prob. 6ACh. 2.1A - a. Complete the following truth table, p q pq p pq...Ch. 2.1A - If q stands for This course is easy and r stands...Ch. 2.1A - Prob. 9ACh. 2.1A - Write the negation of each statement in exercise...Ch. 2.1A - For each of the following, is the pair of...Ch. 2.1A - Describe Dr. No as completely as possible.Ch. 2.1A - Write each of the following in symbolic form if p...Ch. 2.1A - For each of the following implications, write the...Ch. 2.1A - Prob. 15ACh. 2.1A - Write a statement logically equivalent to the...Ch. 2.1A - Investigate the validity of each of the following...Ch. 2.1A - Use the truth table below to prove the chain rule...Ch. 2.1A - Prob. 19ACh. 2.1A - For each of the following, form a conclusion that...Ch. 2.1A - Write the following in if-then form. a. Every...Ch. 2.1A - Use De Morgans Laws to write a negation of each of...Ch. 2.1B - Determine which of the following are statements...Ch. 2.1B - Use the quantifiers to make each of the following...Ch. 2.1B - Use the quantifiers to make each equation in...Ch. 2.1B - Write the negation of each of the following...Ch. 2.1B - Identity the following as true or false. a. For...Ch. 2.1B - a. If you know that p is true, what can you...Ch. 2.1B - If q stands for You said goodbye and r stands for...Ch. 2.1B - Decide on the truth value of each of the following...Ch. 2.1B - Write the negation of each statement in exercise...Ch. 2.1B - For each of the following, is the pair of...Ch. 2.1B - Use the Euler diagram to describe Ms. Makeover as...Ch. 2.1B - Write each of the following in symbolic form if p...Ch. 2.1B - For each of the following implications, state the...Ch. 2.1B - Iris makes the true statement If it rains, then I...Ch. 2.1B - Investigate the validity of each of the following...Ch. 2.1B - For each of the following, form a conclusion that...Ch. 2.1B - Write each of the following in if-then form. a....Ch. 2.1B - Use De Morgans laws to write a negation of each of...Ch. 2.1B - Use the chain rule to form a logical conclusion...Ch. 2.2 - Prob. 1MCCh. 2.2 - Prob. 2MCCh. 2.2 - Prob. 3MCCh. 2.2 - Explain why {} has as an element and also as a...Ch. 2.2 - Prob. 5MCCh. 2.2 - Explain why the word finite was used in the...Ch. 2.2 - Define less than or equal to in a way similar to...Ch. 2.2 - Prob. 8MCCh. 2.2 - Draw a Venn diagram depicting A. Shade A. What is...Ch. 2.2 - A set has elements in an arithmetic sequence...Ch. 2.2 - A set of 100 people on a tour include only men and...Ch. 2.2 - Prob. 12MCCh. 2.2 - A student asks if A is a subset of B and B is a...Ch. 2.2 - A student states that given any two sets A and B,...Ch. 2.2 - Prob. 15MCCh. 2.2 - Review Problems If p is false and q is true, find...Ch. 2.2 - Prob. 17MCCh. 2.2 - Review Problems Complete the following truth...Ch. 2.2 - Prob. 1NAEPCh. 2.2A - Write the following sets using the listing roster...Ch. 2.2A - Rewrite the following using mathematical symbols,...Ch. 2.2A - Which of the following pairs of sets can be placed...Ch. 2.2A - Prob. 4ACh. 2.2A - Prob. 5ACh. 2.2A - Which of the following represent equal sets?...Ch. 2.2A - Find the cardinal number of the each of the...Ch. 2.2A - If U is the set of all college students and A is...Ch. 2.2A - Suppose B is a proper subset of C. a. If n(C)=8,...Ch. 2.2A - Prob. 10ACh. 2.2A - Prob. 11ACh. 2.2A - Prob. 12ACh. 2.2A - Identify all the possible proper subset...Ch. 2.2A - Indicate which symbol, or , makes each of the...Ch. 2.2A - Indicate which symbol, or _, makes each of the...Ch. 2.2A - Assessment Answer each of the following. If your...Ch. 2.2A - Use the definition of less than to show each of...Ch. 2.2A - On a certain senate committee there are seven...Ch. 2.2A - Name two infinite sets that are equivalent but not...Ch. 2.2A - Write an argument to show that the set of even...Ch. 2.2A - Draw a Venn diagram showing the relationship...Ch. 2.2A - Prob. 22ACh. 2.2A - If the set of officers of the Adamsville Beta Club...Ch. 2.2B - Prob. 1ACh. 2.2B - Prob. 2ACh. 2.2B - Which of the following pairs of sets can be placed...Ch. 2.2B - How many one-to-one correspondences exist between...Ch. 2.2B - Prob. 5ACh. 2.2B - Prob. 6ACh. 2.2B - Prob. 7ACh. 2.2B - Prob. 8ACh. 2.2B - Suppose AB. a. Explain why n(A) could equal 0. b....Ch. 2.2B - Prob. 10ACh. 2.2B - Prob. 11ACh. 2.2B - If a set has 16 subsets, how many elements are in...Ch. 2.2B - Identify all the possible proper subset...Ch. 2.2B - Indicate which symbol, or , makes each of the...Ch. 2.2B - Answer each of the following. If your answer is...Ch. 2.2B - Use the definition of lessthan to show each of the...Ch. 2.2B - Prob. 17ACh. 2.2B - Prob. 18ACh. 2.2B - Write an argument showing that the set of whole...Ch. 2.2B - Draw a Venn diagram showing the members of...Ch. 2.2B - In a state swim meet, if the set of swimmers in...Ch. 2.2B - Prob. 22ACh. 2.2B - Prob. 23ACh. 2.2B - Prob. 24ACh. 2.3 - Prob. 2MCCh. 2.3 - Prob. 3MCCh. 2.3 - Prob. 5MCCh. 2.3 - Prob. 6MCCh. 2.3 - Describe a real- life situation that can be...Ch. 2.3 - Prob. 8MCCh. 2.3 - In small groups, identify three characteristics...Ch. 2.3 - A student asks, If A={a,b,c} and B={b,c,d}, why...Ch. 2.3 - Prob. 11MCCh. 2.3 - A student argues that adding two sets A+B, and...Ch. 2.3 - Prob. 13MCCh. 2.3 - Describe the contrapositive of the contrapositive...Ch. 2.3 - Write a conclusion for each of the following...Ch. 2.3 - Prob. 16MCCh. 2.3 - Prob. 17MCCh. 2.3 - Find the number of elements in the following sets:...Ch. 2.3 - Prob. 19MCCh. 2.3 - Prob. 20MCCh. 2.3 - Prob. 21MCCh. 2.3 - Prob. 1NAEPCh. 2.3A - Prob. 1ACh. 2.3A - Prob. 2ACh. 2.3A - Prob. 3ACh. 2.3A - If BA find a simpler expression for each of the...Ch. 2.3A - Prob. 5ACh. 2.3A - Prob. 6ACh. 2.3A - For each of the following conditions, find AB. a....Ch. 2.3A - Prob. 8ACh. 2.3A - Prob. 9ACh. 2.3A - Prob. 10ACh. 2.3A - Prob. 11ACh. 2.3A - Prob. 12ACh. 2.3A - a. If A has three elements and B has two elements,...Ch. 2.3A - If n(A)=4, n(B)=5, and n(C)=6, what is the...Ch. 2.3A - In 2012, the population of the United States was...Ch. 2.3A - Assessment Given that the universe is the set of...Ch. 2.3A - Prob. 17ACh. 2.3A - In a sorority with 40 members, 18 take...Ch. 2.3A - In Pauls bicycle shop, 50 bicycle were inspected....Ch. 2.3A - The Red Cross looks for three types of antigens in...Ch. 2.3A - John has applied for the registrars job at small...Ch. 2.3A - Three announcers each try to predict the winners...Ch. 2.3A - The table below contains the 10 most popular candy...Ch. 2.3A - When the Titanic sank, the following data about...Ch. 2.3A - Two families, each having three children, are at a...Ch. 2.3A - Let A={x,y} and B={a,b,c}.Find each of the...Ch. 2.3A - For each of the following, the Cartesian product...Ch. 2.3B - Assessment If W={0,1,2,3,.......},...Ch. 2.3B - Prob. 2ACh. 2.3B - Prob. 3ACh. 2.3B - If XY, find a simpler expression for each of the...Ch. 2.3B - Prob. 5ACh. 2.3B - Prob. 6ACh. 2.3B - For each of the following conditions, find BA. a....Ch. 2.3B - Prob. 8ACh. 2.3B - Prob. 9ACh. 2.3B - Prob. 10ACh. 2.3B - In a police bulletin, it was reported that a...Ch. 2.3B - Assessment a. If n(AB)=23, n(AB)=9, and n(B)=12,...Ch. 2.3B - The equation AB=AB and a similar equation for AB...Ch. 2.3B - Prob. 14ACh. 2.3B - Fill in the Venn diagram with the appropriate...Ch. 2.3B - Prob. 16ACh. 2.3B - Students at Hellgate High School were asked if...Ch. 2.3B - A pollster interviewed 600 university seniors who...Ch. 2.3B - In a survey of 1000 investors, it was determined...Ch. 2.3B - In a survey of 150 students, 90 were taking...Ch. 2.3B - Prob. 21ACh. 2.3B - Assessment At the end of a tour, several guides...Ch. 2.3B - Tell whether each of the following is true or...Ch. 2.3B - Prob. 24ACh. 2.CR - Write an example of a statement and an example of...Ch. 2.CR - Explain the difference between the following two...Ch. 2.CR - Which of the following are statements? a. 3+5=9 b....Ch. 2.CR - Negate each of the following; a. No women smoke b....Ch. 2.CR - Write the converse, inverse and contrapositive of...Ch. 2.CR - Use the truth table to show that pqqp,Ch. 2.CR - Construct truth tables for each of the following....Ch. 2.CR - Prob. 8CRCh. 2.CR - Write the following argument symbolically and then...Ch. 2.CR - Prob. 10CRCh. 2.CR - Prob. 11CRCh. 2.CR - Prob. 12CRCh. 2.CR - Prob. 13CRCh. 2.CR - Prob. 14CRCh. 2.CR - Prob. 15CRCh. 2.CR - a. If D={t,h,e} and E={e,n,d}, show one possible...Ch. 2.CR - Prob. 17CRCh. 2.CR - If AB, which of the following are always true?...Ch. 2.CR - Tell whether each of the following is true or...Ch. 2.CR - Prob. 21CRCh. 2.CR - Decide whether each of the following is always...Ch. 2.CR - Prob. 23CRCh. 2.CR - If n(A)=3, n(B)=4 and n(C)=2, find n((AB)C)Ch. 2.CR - Case Eastern Junior College awarded 26 varsity...Ch. 2.CR - According to a student survey, 16 students liked...Ch. 2.CR - Prob. 27CRCh. 2.CR - Heidi has a brown pair and grey pair of slacks; a...Ch. 2.CR - Prob. 29CRCh. 2 - NOW TRY THIS a. Use truth tables to prove Theorem...Ch. 2 - NOW TRY THIS Build a truth table to determine when...Ch. 2 - Prob. 3NTCh. 2 - Prob. 4NTCh. 2 - NOW TRY THIS Explain why there can be no greatest...Ch. 2 - Prob. 6NTCh. 2 - Prob. 8NT
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