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nature of mathematics

Questions and Answers of Nature Of Mathematics

Answer each of the given true/false questions.A = {American manufactured automobiles}C = {Chevrolet, Cobalt, Corvette}R = {Colors in the rainbow}S = {red, orange, yellow, green, blue, indigo,
Find all possible subsets of C = {5, 7}.
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.a.b.c. (2, 5, 8) U (3, 6, 9} 8}
Tell whether each set in Problems 5–8 is well defined. If it is not well defined, change it so that it is well defined.a. {Counting numbers less than 0}b. The set of people with pointed ears
Find the proper and improper subsets of A = {2, 4, 6, 8}. What is the cardinality of A?
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.a.b.c. {1, 2, 3, 4, 5} n {3, 4, 5, 6, 7}
Specify the sets in Problems 9–14 by roster.a. {Distinct letters in the word mathematics}b. {Current U.S. president}
Name the regions in Figure 2.6 described by each of the following.a. Ab. Cc. Ad. B̅e. A ⊆ Bf. A and C are disjoint U I A IV V VII III B VI II VIII
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.a.b.c. {1, 2,5} n {7,9}
Specify the sets in Problems 9–14 by roster.a. {Odd counting numbers less than 11}b. {Positive multiples of 3}
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {2, 4, 6, 8, 10}
Specify the sets in Problems 15–20 by description.{1, 2, 3, 4, 5, 6, 7, 8, 9}
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {x|x is a multiple of 3} n {x|x is a multiple of 5}
Specify the sets in Problems 15–20 by description.{1, 11, 121, 1331, 14641,...}
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {x|x is even}
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {yly is odd}
Specify the sets in Problems 15–20 by description.{10, 20, 30, ... , 100}
Specify the sets in Problems 15–20 by description.{50, 500, 5000, ...}
Perform the given set operations in Problems 19–24. {x|x is a positive integer) U {x|x is a negative integer}
Perform the given set operations in Problems 19–24. {x|x is a positive integer} n {x|x is a negative integer}
Specify the sets in Problems 15–20 by description.{101, 103, 105, ... , 169}
Specify the sets in Problems 15–20 by description.{m, i, s, p}
Perform the given set operations in Problems 19–24.a.b. NUW
Write out in words the description of the sets given in Problems 21–26, and then list each set in roster form.{x | x is an odd counting number}
Perform the given set operations in Problems 19–24.a. U̅b. ∅̅
Write out in words the description of the sets given in Problems 21–26, and then list each set in roster form.{x | x is a natural number between 1 and 10}
Perform the given set operations in Problems 19–24.a. X ∩ ∅ for any set Xb. X ∪ ∅ for any set X
Write out in words the description of the sets given in Problems 21–26, and then list each set in roster form.{x | x ∈ N, x ≠ 86}
Perform the given set operations in Problems 19–24.a. U ∪ ∅b. U ∩ ∅
Write out in words the description of the sets given in Problems 21–26, and then list each set in roster form.{x | x ∈ W, x ≤ 86}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.A ∪ B
Write out in words the description of the sets given in Problems 21–26, and then list each set in roster form.{x | x ∈ W, x < 86}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.A ∩ B
Write out in words the description of the sets given in Problems 21–26, and then list each set in roster form.{x | x ∈ W, x ∉ E} where E = {2, 4, 6,...}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.A ∪ C
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.All even numbers
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.A ∩ C
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.All positive multiples of 5
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.B ∩ C
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.All counting numbers between 0 and 10
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {x|x is a multiple of 3} U {x|x is a multiple of 5}
Specify the sets in Problems 9–14 by roster.a. {Counting numbers containing only 1s}b. {Even counting numbers between 5 and 15}
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {x|x is a multiple of 2} {x|x is a multiple of 3}
Specify the sets in Problems 9–14 by roster.a. {Distinct letters in the word pipe}b. {Counting numbers greater than 150}
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {x|x is a multiple of 2} U {x|x is a multiple of 3}
Specify the sets in Problems 9–14 by roster.a. {C | C is an integer greater than 6}b. {B | B is an integer less than 6}
Perform the given set operations in Problems 7–18.Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. {1, 3, 5, 7,9}
Specify the sets in Problems 9–14 by roster.a. {A | A is a counting number greater than 6}b. {B | B is a counting number less than 6}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.B ∪ C
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.{3, 6, 9, 12, ...}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.A̅
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.{... , 210, 25, 0, 5, ...}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.B̅
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.{A, E, I, O, U}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.C̅
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.{x | x = 4n, n a counting number}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.U̅
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40. {x|x is greater than 4}
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.{x |-5 ≤ n ≤ 5, n a counting number}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40. {yly is between 4 and 10}
Sets can be written by description, roster, or set builder-notation. In Problems 27–35, write each given set in two alternative ways.{n | n > 100, n a counting number}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40. {x|x is less than 5} U {x|x is greater than 5}
List all possible subsets of the given set.a. A = Φb. B = {1}c. C = {1, 2}d. D = {1, 2, 3}e. E = {1, 2, 3, 4}
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40. {x|x is less than 5} {x|x is greater than 5}
List all possible subsets of the given set.a. G = Φb. H = {6}c. I = {6, 7}d. J = {6, 7, 8}e. K = {6, 7, 8, 9}
Look for a pattern in Problem 36. Can you guess how many subsets the set F = {1, 2, 3, 4, 5} has? Does this guess match the formula?Data from Problem 36List all possible subsets of the given set.A =
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.∅ ∪ A
Look for a pattern in Problem 37. Can you guess how many subsets the set L = {6, 7, 8, 9, 10} has? Does this guess match the formula?Data from Problem 37List all possible subsets of the given set.G =
Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}. List all the members of each of the sets in Problems 25–40.∅ ∩ B
In Problems 41–46, use set notation to identify the highlighted region. U A B
Draw a Venn diagram showing people who are over 30, people who are 30 or under, and people who drive a car.
In Problems 41–46, use set notation to identify the highlighted region. U B
Draw a Venn diagram showing males, females, and those people who ride bicycles.
In Problems 41–46, use set notation to identify the highlighted region. U A B
Draw a Venn diagram showing that all Chevrolets are automobiles.
In Problems 41–46, use set notation to identify the highlighted region. U A B
Draw a Venn diagram showing that all cell phones are communication devices.
In Problems 41–46, use set notation to identify the highlighted region. U B
Consider the setsA = {distinct letters in the word pipe}B = {4}C = {p, i, e}D = {2 + 1}E = {three}F = {3}a. What is the cardinality of each set?b. Which of the sets are equivalent?c. Which of the
In Problems 41–46, use set notation to identify the highlighted region. U B
Consider the setsA = {16}B = {10 + 6}C = {10, 6}D = {25}E = {2, 5}a. What is the cardinality of each set?b. Which of the sets are equivalent?c. Which of the given sets are equal?
Draw Venn diagrams for each of the relationships in Problems 47–52.X ∪ Y
Draw Venn diagrams for each of the relationships inProblems 47–52.X ∩ Y
Draw Venn diagrams for each of the relationships inProblems 47–52.X ∩ Z
Draw Venn diagrams for each of the relationships inProblems 47–52.X ∪ Z
Draw Venn diagrams for each of the relationships inProblems 47–52.Y̅
Draw Venn diagrams for each of the relationships inProblems 47–52.Z̅
Decide whether each statement in Problems 46–54 is true or false. Give reasons for your answers.a. 1 ∈ {{1}, {2}, {3}, {4}}b. {1} ∈ {{1}, {2}, {3}, {4}}
Montgomery College has a 50-piece band and a 36-piece orchestra. If 14 people are members of both the band and the orchestra, can the band and orchestra travel in two 40-passenger buses?
Decide whether each statement in Problems 46–54 is true or false. Give reasons for your answers.a. {1} ⊂ {{1}, {2}, {3}, {4}}b. 0 = { }
Decide whether each statement in Problems 46–54 is true or false. Give reasons for your answers.a. ∅ = { }b. {∅} = { }
From a survey of 100 college students, a marketing research company found that 75 students owned iPods, 45 owned cars, and 35 owned both cars and iPods.a. How many students owned either a car or an
Give an example of a set that cannot be written using the roster method.
In a survey of a TriDelt chapter with 50 members, 18 were taking mathematics, 35 were taking English, and 6 were taking both. How many were not taking either of these subjects?
Is it possible to list the set of rational numbers between 0 and 1 by roster? If you think so, then list them, and if you do not think so, explain why.
In a senior class at Rancho Cotati High School, there were 25 football players and 16 basketball players. If 7 persons played both sports, how many different people played in these sports?
Five people plan to meet after school, and if they all show up, there will be one group of five people. However, if only four of them show up, in how many ways is this possible?
The fire department wants to send booklets on fire hazards to all teachers and homeowners in town. How many booklets does it need, using these statistics?50,000 homeowners 4,000 teachers 3,000
Five people plan to meet after school, and if they all show up, there will be one group of five people. However, if only three of them show up, in how many ways is this possible?
Working in small groups is typical of most work environments, and being able to work with others to communicate specific ideas is an important skill to learn. At the end of each chapter is a list of

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