Math

Determine whether the following statement is true or false. 33∉​{1, 2, 3,​ ..., 40}

False

Determine whether the set is finite or infinite. The set of natural numbers less than 4.

the set is finite with a cardinality of 3

Write a word description of the set. ​{10, 11,​ 12, 13,​ ...}

the set of natural numbers greater than 9

Write a word description of the set. ​{10, 11,​ 12, 13,​ ...}

the set of natural numbers greater than 9 Your answer is correct.

Express the set using the roster method. {x|x is a month that begins with A}

{April, August}

Express the set using​ set-builder notation. Use inequality notation to express the condition x must meet in order to be a member of the set. {36, 37, 38, 39, ..., 57}

{x∈N and 36≤x≤57}

Construct a Venn diagram illustrating the given sets. A​ = {19, 24, 29, 39}​, B​ = {4, 9, 19, 24, 29, 34}​, C​ = {14, 19, 34}​, U​ = {4, 9, 14, 19, 24, 29, 34, 39, 44} Find the Venn diagram that illustrates the given sets. Choose the correct answer below.

B

Use the Venn diagram to represent the set B′ in roster form.

B' = 1, 4, 22, 26

Determine whether ⊆​, ⊂​, ​both, or neither can be placed in the blank to make the statement true. ​{M​,R​,T​} ​___ ​{M​, R​, T​, V​}

Both ⊆ & ⊂

Use the Venn diagram shown to the right to list the set C in roster form.

C = 11, 12, 13, 14, 16

Let U = ​{q,r,s,t,u,v,w,x,y,z}, A = ​{q,s,u,w,y}, B = ​{q,s,y,z}, and C = ​{v,w,x,y,z}. List the elements in the set A ∪ (B ∩ C).

C. A ∪ (B ∩ C) = ​{q,s,u,w,y,z}

A winter resort took a poll of its 350 visitors to see which winter activities people enjoyed. The results were as​ follows: 212 people liked to​ ski, 229 people liked to​ snowboard, and 153 people liked to ski and snowboard. How many people in the poll liked to ski or​ snowboard?

288 liked to ski or snowboard

Write ⊆ or ⊈ in the blank so that the resulting statement is true. ​{t, h, e, m, o, r, s, e, c, o, d, e​}_______{h, e, r, e, c, o, m, e, d, o, t, s​} because

​{t, h, e, m, o, r, s, e, c, o, d, e​}is a subset of ⊆​ {h, e, r, e, c, o, m, e, d, o, t, s​} because all of the elements in the first set are in the second set

B = {x | xEN and 2 < x < 12}

n(B) = 10

Although you want to choose a career that fits your interests and​ abilities, it is good to have an idea of what jobs pay when looking for career options. The bar graph shows the average yearly earnings of​ full-time employed college graduates with only a​ bachelor's degree based on their college​ major, in a certain year. Use the information given by the graph to represent the following set by the roster method. {x x is a major with $38,000<average yearly earnings≤$53,000}

​{Nursing​, Journalism​, Social Work​}

List all the subsets of the given set. {e, q, t} Choose the answer that lists all of the subsets of {e, q, t}.

​{}, ​{e​}, {q​}, ​{t​}, {e​,q​}, {e​, t​}, {q​,t​}, ​{e​, q​, t​}

Write ⊆ or ⊈ in each blank so that the resulting statement is true. ∅​_______{2,4,6,8​}

∅ is a subset of⊆ {2,4,6,8​}

Determine whether ⊆​, ⊂​, ​both, or neither can be placed in each blank to form a true statement. ​{x|x is someone who is not tall or someone who is tall​}_______{x|x is a​ person}

⊆

Select ⊆ or ⊈ for the blank so that the resulting statement is true. ​{ 6​, 1​, 3 ​} ___​ { ​1, 2,​ ..., 6 ​}

⊆

Select ⊆ or ⊈ for the blank so that the resulting statement is true. ​{ −7​, ​0, 7 ​} ___​ { −7​, −5​, 5​, 7 ​}

⊈

Write ⊆ or ⊈ in each blank so that the resulting statement is true. ​{x|x is a bear​}_______{x|x is a black bear​}

⊈

Although you want to choose a career that fits your interests and​ abilities, it is good to have an idea of what jobs pay when looking for career options. The bar graph shows the average yearly earnings of​ full-time employed college graduates with only a​ bachelor's degree based on their college major. Use the information given by the graph to represent the following set by the roster method. The set of college majors with average yearly earnings that exceed ​$57​,000.

{Accounting, Engineering}

Find the cardinal number for the given set. A={5, 7, 9, 11, 19, 18}

6 (six)

Use the Venn diagram to represent A in roster form

A = 1, 5, 7, 12

Use the Venn diagram to represent the set A ∩ B in roster form.

A ∩ B = 9, 11

Use the Venn diagram to represent the set A ∩ B′ in roster form.

A ∩ B′ = 1, 6

Let U={x | x ∈N and x<7} A={x | x is an odd natural number and x<7} B={x | x is an even natural number and x<7} C={x | x ∈ N and 1<x<4} Find the set A ∩ U.

A ∩ U = 1, 3, 5

Find the set A ∩ U. U = {f, g, h, i, j, k, l, m, n} A = {f, l, m} B = {g, m, n} C = {f, h, i, j, n}

A ∩ U = f, l, m

Let U={x | x ∈N and x<6} A={x | x is an odd natural number and x<6} B={x | x is an even natural number and x<6} C={x | x ∈ N and 1<x<3} Find the set A ∪ B.

A ∪ B = 1, 2, 3, 4, 5

Find set A′ ∩ B′ U={1, 2, 3, 4, 5, 6, 7} A={1, 2, 3, 4} B={3, 4, 5}

A′ ∩ B′ = 6,7

Use the Venn diagram to represent the set (A ∪ B)′ in roster form.

(A ∪ B)′ = 22, 26

Determine whether the following statement is true or false. If the statement is​ false, make the necessary​ change(s) to produce a true statement.

D⊆P.

Determine whether the statement is true or false. 15∈{x | x∈N and 18≤x<34}

False

determine whether the statement is true or false. 21∈{4,5,6,...17}

False​, because 21 is not a natural number greater than or equal to 4 and less than or equal to 17.

A math tutor working with a small group of students asked each student when he or she had studied for class the previous weekend. Their responses are shown in the Venn diagram. Use the Venn diagram to list the set of students who studied Saturday and not Sunday in roster form.

Hanna

Write a word description of the set. ​{January, February,​ March, April,​ May, June,​ July, August,​ September, October,​ November, December}

Months of the year

A palindromic number is a natural number whose value does not change if its digits are reversed. Examples of palindromic numbers are​ 11, 454, and 261162. Use this definition to place 101 in the correct region of the Venn diagram where U is the set of natural​ numbers, A is the set of palindromic​ numbers, and B is the set of even numbers.

Region 1

The bar graph on the right shows the percentage of students at a local high school with preferences for various careers. Career E is elementary school​ teacher, P is police​ officer, B is​ banker, S is​ surgeon, A is airline​ pilot, F is family​ doctor, and L is lawyer. Use the graph to place the police officer career in the correct region of the Venn​ diagram, also on the​ right, where U is the set of​ careers, A is the set of careers for which more than​ 20% of students are considering as a​ career, and B is the set of careers for which more than​ 20% of students are not considering as a career.

Region 1

Set A is a subset of set​ B, expressed as​ _______, means that​ _______.

Set A is a subset of set​ B, expressed as A⊆​B, means that every element in set A is also an element in set B

Louise wants to visit Austin, Columbus, Baltimore, Memphis​, Chicago​, Boston​, San Jose​, Phoenix​, El Paso​, and San Antonio. If she decides to visit​ some, all, or none of these​ cities, how many travel options does she ​have?

She has 1,024 travel options

For the given​ set, first calculate the number of subsets for the​ set, then calculate the number of proper subsets. ​{ 19​, 11​, 4​, 2 ​}

The number of subsets is 16. The number of proper subsets is 15.

Determine if the set is the empty set. {x | x<10 and x>15}

The set is the empty set.

Determine if the set is the empty set. {x | x<6 and x>15}

The set is the empty set.

Determine whether the following statement is true or false. If the statement is​ false, make the necessary​ change(s) to produce a true statement. The set of subsets of {1, 7, 10, 13, 16, 19, 22} contains 256 elements.

The statement should be changed to​ "The set of subsets of {1, 7, 10, 13, 16, 19, 22} contains 128 elements

Houses in an estate are all identical.​ However, a person can purchase a new house with​ some, all, or none of a set of​ options, as indicated by the set below. How many options are there for purchasing a house in this​ community? ​{upgraded landscaping, alarm system, screened-in balcony, lake view, pool​}

There are 32 options for purchasing a house in the community.

Use the Venn diagram to represent set U in roster form.

U = 2, 5, 8, 10, 14, 16, 19, 23, 25

A fast food chain is thinking of opening a new restaurant location. The company conducts a market survey of students from the nearby college campus to determine their interest in new fast food restaurants. They ask the students surveyed to identify which fast food restaurants are the best. Is the set of​ 'best fast food​ restaurants' well-defined? (Y/N)

Yes

A is the set of students at your college. B is the set of students majoring in statistics at your college. Complete parts​ (a) and​ (b) below

a. Are the sets​ equivalent? Explain. Set A is not equivalent to set​ B, because set A and set B do not contain the same number of elements. Part 2 b. Are the sets​ equal? Explain. Set A is not equal to set​ B, because set A and set B do not contain exactly the same elements, regardless of order or repetition of elements.