A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
12th Edition
ISBN: 9780321987297
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Chapter 2.2B, Problem 20A
Draw a Venn diagram showing the members of Congress of United States, the member of the House Representative, and the members of the Senate.
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Chapter 2 Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
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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- A survey of 300 workers yielded the following information: 231 workers belonged to a union and 195 were Democrats. If 172 of the union members were Democrats, how many workers were neither belonged to a union nor were Democrats?arrow_forwardThere are 100 students who are taking history or sociology. If 10 are taking both courses and 45 are taking just history, how many are taking sociology? Why is it not 45? Use a venn diagram for this problem.arrow_forwardA travel agent surveyed 100 people to find out how many of them had visited the cities of Bacolod and Victorias. Thirty-one people had visited Bacolod, 26 people had been to Victorias, and 12 people had visited both cities. Draw a Venn diagram to find the number of people who had visited: a. Bacolod or Victorias b. Victorias but not Bacolod c. Only one of the cities d. Neither cityarrow_forward
- An online music service surveyed 500 customers and found that 270 listen to hip-hop music, 320 listen to rock, and 160 listen to country. In addition, 140 listen to both rock and hip-hop, 120 listen to rock and country, and 80 listen to hip-hop and country. Finally, 50 listen to all three. Draw a Venn diagram to represent the results of the survey and find the number of customers who: A. Listen to only hip-hop. B. Listen to rock and country but not hip-hop. C. Don't listen to any of these three types of music. D. Don't listen to country music.arrow_forward4. A survey was conducted for 1000 people. Apparently 595 members of the democratic party, 595 wearing glasses and 550 love ice cream: 395 of them are members of the democrat party wearing glasses, 350 members of the ice-cream democratic party, and 400 people wearing glasses and love ice cream, 250 of them are members of the democratic party who wear glasses and love ice cream. A). How many of them are democrats, do not wear glasses and do not like ice cream? B). How many of them are democratic party members but do not wear glasses and do not like ice cream?arrow_forwardIn an examination for final year students of a school, 60 offered Mathematics, 50 offered Economics and 48 offered Geography. 30 offered Mathematics and Economics, 16 offered Mathematics and Geography. and 22 offered Economics and Geography. If 10 candidates offered all the three subjects. a. Find the number of students offering only one subject. b. Find the number of students offering only two subjects.arrow_forward
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