Chapter 2 MGF 1106

B={x|21<x<(line underneath)24} ​1. Write set B in roster form. Choose the correct answer below. A. A={22, 23, 24} B. A=(22, 23, 24, 25} C. A={22, 23, 24,...} ​2. Can set B be written in roster​ form? Explain your answer. Choose the correct answer below. A. Yes, the roster form of set B is Upper B equals StartSet 21 comma ... 22 comma ... 23 comma ... 24 EndSet. B. No, set B cannot be written in roster form because the last number in the set cannot be determined. C. Yes, the roster form of set B is similar to the roster form of set A. D. No, set B cannot be written in roster form because set B contains an infinite number of elements. E. No, set B cannot be written in roster form because there is an infinite number of elements between any two elements in set B.

1. A={22, 23, 24} 2. E. No, set B cannot be written in roster form because there is an infinite number of elements between any two elements in set B.

The expression for determining the number of distinct subsets for a set with n distinct elements is

2^n

A={x|x E(Symbol)N and x >11} B={x|x >11} ​A) Write a description of set A and set B. Start with set A. Choose the correct answer below. A. Set A is the set of all-natural numbers less than 11. B. Set A is the set of all numbers greater than 11. C. Set A is the set of all-natural numbers greater than or equal to 11. D. Set A is the set of all-natural numbers greater than 11. B) Now determine the description of set B. Choose the correct answer below. A. Set B is the set of all numbers greater than or equal to 11. B. Set B is the set of all numbers less than or equal to 11. C. Set B is the set of all numbers greater than 11. D. Set B is the set of all numbers less than 11.

A) D. Set A is the set of all natural numbers greater than 11. B) C. Set B is the set of all numbers greater than 11.

Express the following set in​ set-builder notation. C is the set of days with Upper W in their name. A. C= {x|x is wednesday} B. C= {wednesday} C. C= {x|x is W} D. C= {x|x is wednesday or x is saturday} E. C= {x|x is saturday} F. C= {}

A. C= {x|x is Wednesday}

Determine whether the number used is a cardinal number or an ordinal number. Mary Garcia has directed her eighth movie. A. In this​ context, the word ​"eighth​" is used as an ordinal number because it describes the relative position of the movie. B. In this​ context, the word ​"eighth​" is used as an ordinal number because it answers the question​ "How many movies has Mary nothingGarcia directed​?" C. In this​ context, the word ​"eighth​" is used as a cardinal number because it answers the question​ "How many movies has Mary nothingGarcia directed​?" D. In this​ context, the word ​"eighth​" is used as a cardinal number because it describes the relative position of the movie.

A. In this​ context, the word ​"eighth​" is used as an ordinal number because it describes the relative position of the movie.

Determine whether the pair of sets is​ equal, equivalent,​ both, or neither. A= {literature, biology, calculus} B= {biology, calculus, literature} A. both B. neither C. equivalent D. equal

A. both n(A)=3 N(B)=3 Set A and B equivalent Do they contain the same elements? Set A and B equal

Determine whether the pair of sets is​ equal, equivalent,​ both, or neither. A= {biology, geometry, trigonometry} B= {geometry, physics, trigonometry, biology} A. neither B. equivalent C. both D. equal

A. neither n(A)= 3 n(B)=4 not equivalent not equal since physics is not in both

The accompanying list shows the​ attendance, in​ millions, at the 10 most visited museums in the world in 2008. Use the list to determine the given set in roster form. The set of museums in which the attendance was between 4 million and 5 million Museum Attendance​ (in millions) A 7.83 B 6.13 C 4.97 D 4.95 E 4.65 F 4.47 G 4.34 H 3.19 I 2.95 J 2.55 Choose the correct answer below. A. {C, D, E, F, G​} B. {B, C, D, E} C. {A, B, H, I, J} D. {C, G} E. {A, B, C, D, E, F, G, H, I, J} F. {empty set} circle with a line through it

A. {C, D, E, F, G}

A={x|x E(Symbol)N and x >11} B={x|x >11} C) Explain the difference between set A and set B. Choose the correct answer below.​ (Hint: is 47 1/2 E(symbol)of A? Is 47 1/2 E(symbol)B? A. Set A contains only positive numbers. Set B contains other types of numbers including negative numbers. B. Set A contains only natural numbers. Set B contains other types of numbers including fractions and decimals. C.Set A contains only natural numbers. Set B contains only numbers that are not natural numbers. D.Set B is the same as set A but written in a more concise form. ​D) Write set A in roster form. Choose the correct answer below. A. A={11, 12, 13, 14,...} B. A={12, 13, 14, 15} C. A={12, 13, 14, 15,...} D. A={1, 2, 3, 4,..., 11} E. Set A cannot be written in roster form.

C) B. Set A contains only natural numbers. Set B contains other types of numbers including fractions and decimals. D) C. A={12, 13, 14, 15,...}

Describe three sets that have no members. Select all that apply. A.The set of all odd numbers between 100 and 110 that are a multiple of 3. B.The set of all months whose name contains the letter V. C.The set of all even prime numbers larger than 27. D.The set of all negative integers larger than 16. E.The set of all days whose name does not end in the letter Y. F.The set of states in the United States that have a common border with Massachusetts. G.The set of all fractions between 1 and 2.

C,D,E

Express the following set in​ set-builder notation. B= {11, 12, 13, 14, 15, 16, 17, 18} A. B={x|xE(symbol)N and 11<x<18} B. B={x|xE(symbol)N and 11< with line less than or equal to x<18} C. B={x|xE(symbol)N and 11< (with line)x<(with line)18} D. B={x|xE(symbol)N and 11<x<(with line)18}

C. B={x|xE(symbol)N and 11< (with line)x<(with line)18}

Express the following set in​ set-builder notation. E is the set of odd integers. A. E={x|xE(symbol)N and x is odd} B. E={x|xE(symbol)N and x is even} C. E={x|x is n integer and x is odd} D. E={x|xE(symbol)N and x is a multiple of 4} E. E={x|xE(symbol)N} F. E= (empty set) circle with a line in it

C. E={x|x is n integer and x is odd} All the elements in E are integers because E is the set of even integers.

Determine whether the number used is a cardinal number or an ordinal number. Anne A. Johnson has written 9 books. A. In this​ context, the number 9 is used as an ordinal number because it describes the relative position that an element occupies. B. In this​ context, the number 9 is used as an ordinal number because it answers the question​ "How many books has Anne A. Johnson written​?" C. In this​ context, the number 9 is used as a cardinal number because it describes the relative position that an element occupies. D. In this​ context, the number 9 is used as a cardinal number because it answers the question​ "How many books has Anne A. Johnson written​?"

D. In this​ context, the number 9 is used as a cardinal number because it answers the question​ "How many books has Anne A. Johnson written​?"

​A={x|x E(Symbol)N and x >11} B={x|x >11} E) Can set B be written in roster​ form? Explain. Choose the correct answer below. A. No, set B cannot be written in roster form because of the last number in the set cannot be determined. ​B. No, set B cannot be written in roster form because there are an infinite number of elements between any two elements in set B. C. Yes, the roster form of set B is similar to the roster form of set A. D. Yes, the roster form of set B is B={12,...,13,...14...15,...} E. No, set B cannot be written in roster form because set B contains an infinite number of elements

E) B. No, set B cannot be written in roster form because there are an infinite number of elements between any two elements in set B.

Decide if the given statement is true or false. If it is​ false, give the reason. ​{5​, 6​, 8​} is a proper subset of (u turn to the right) ​{6​, 5​, 8​} A. This statement is true. B. This statement is false. The second set is a proper subset of the first​ set, not the other way around. C. This statement is false. The second set does not contain all the elements present in the first set. D. This statement is false. The elements of the two sets are not in the same order. E. This statement is false. No set is a proper subset of itself.

E. This statement is false. No set is a proper subset of itself.

Express the given set in roster form. E={x|xE(symbol)N AND 6<(line underneath)<76}

E= {6, 7, 8, 9, ...,75}

.​{x | x is a time of the day when 1 < average level of happiness less < 2​} What does it mean?

Has to be greater than 1 but less than 2

Determine whether the statement is true or false. 7E(with a line through it){x|xE(symbol)N and x is even}

TRUE

Determine whether the following statement is true or false. pE(symbol)​{p​, f​, b​, t​, q​}

TRUE p is an element of {p,f,b,t,q}

The set of the five worst U.S. cities. Is it well defined or not?

The set is not well defined

The set of U.S. vice presidents. Is it well defined or not?

The set is well defined

A set that contains no elements or the number of elements in the set is a natural number is called ________ set.

a finite set

A collection of objects is called

a set

Three dots placed in a set to show that the set continues in the same manner is called

an ellipsis

The number of elements in a set is called the __________ number of the set.

cardinal

The three ways a set can be written are___________,___________ and ____________.

description, roster form, and set-builder notation

The set that contains no elements is called the ______ set.

empty or null

Two sets that contain the same elements are called _______ sets.

equal

Two sets that contain the same number of elements are called

equivalent

A set that is not finite is called​ a(n) _______ set.

infinite

Determine whether the set is finite or infinite: {40, 48, 56, 64, ...}

infinite

For the set A​ = ​{1, 3, 5, 7, 10​}, determine​ n(A).

n(A)=5 Count the number of elements in the set. There are 5 elements in set A.

For the set D= {2}, determine n(D).

n(D)= 1

If all the elements of set A are also elements of set​ B, then set A is​ a(n) _______ of set B.

subset

Express the set in roster form: B={x|xE(symbol)N and x is a multiple of 4} What does B{x|xE(symbol)N means? A. B= {4, 8, 12, 16, ...} B. B= {8, 12, 16, 20} C. B= {8, 12, 16, 20, ...} D. B= {4} E. B= {4, 8, 12, 16, ..., 400} F. B= {4, 8, 12, 16} G. B= circle with a line through it (empty set)

x is an element of N (natural numbers) ANSWER: A. B={4, 8, 12, 16, ...}

Express the set in roster form: The set of natural numbers between 19 and 191

{20, 21, 22, 23, ..., 190}

The two ways to indicate an empty set are _______ and _______.

{} and circle with line through it (empty set)