Math Test 2 terms & 2.1

What is the empty set

It is the set that contains no elements

What is another name for the empty set

Null set

What do these symbols represent?

The null/empty set

What is an element?

An individual object or member that belongs to a set. Can be numbers, letters, shapes, or other sets

What does this symbol mean?

Is an element of

What does this symbol mean?

Is not an element of

What is a natural number?

It is an infinite whole number
It is NEVER: negative, a fraction, or a decimal

What is a cardinal number

The number of distinct elements in a set

What does this symbol mean?

The cardinal numbers in a set

{0} {Ø} Is this an empty/null set?

No, because it has something in it

How many elements are in this set?

C ={1,1,2,3,4,2,1}

n(C) = 4
There are 4 different elements, you don’t double count the same numbers

How many elements are in this set?
A = {}

n(A) = 0

What is an equivalent set?

It is a set that contains the same number of elements, the numbers do not have to be the same

What is an equal set?

Contains the exact same elements, even if it has more numbers of said elements:
A = 1,1,2,3,
B= 1,2,3

Determine if the collection is not well defined and therefore is not a set.

The collection of U.S. zipcodes

The collection is well defined and therefore it is a set.

Determine if the collection is not well defined and therefore is not a set.

The collection of the five worst MLB players

The collection is not well defined and therefore it is not a set.

*Opinions are subjective and not well defined

Write a description of the set.

{Scorpio,Sagittarius}

A. The set of Zodiac signs that begin with S.

B. The set of Zodiac signs for March and April.

C. The set of Zodiac signs for October and November.

D. The set of Zodiac signs.

A. The set of Zodiac signs that begin with S.

Write a description of the set

{Saturday, Sunday}
A.The set of weekdays.

B.The set of days of the week that have more than 5 letters.

C.The set of days of the week that end with day.

D.The set of days of the week that start with S.

D.The set of days of the week that start with S.

List the elements of the set of all letters in the word

'real’

A. {}

B. {r,l}

C. {r,e,a,l}

D. {real}

C. {r,e,a,l}

What is roster form?

It’s a way of writting a set by listing all its individual elements inside curly brackets, with each item separated by a comma.

{1,2,3}

What is a subset?

A subset is a set that’s completely contained within another set. There cannot be any elements in a subset which are not also in that other set

What does this symbol represent?

It represents a subset

What does this mean?

A⊆B

A is a subset of B
Every element in A is also in B

A={1,2,3}

B={1,1,2,3}

What does this symbol represent?

It represents a proper subset

What does this mean?
A⊂B

A is a proper subset of B
Every element in A is also in B, but they do not have the same elements

A={1,2,3}

B={1,2,3,4,5}

What is a proper subset?

Express the given set using the roster method.

The set of natural numbers less than 7
A. {7,8,9,10}
B. {1,2,3,4,5,6}

C. {-1,0,1,2,3,4,5,6}

D. {1,2,3,4,5,6,7}

B. {1,2,3,4,5,6}

Determine if the given set is the empty set.

{0,Ø}
A. {0,Ø} is the empty set
B. {0,Ø} is not the empty set

B. {0,Ø} is not the empty set

A. The set is the empty set.

B. The set is not the empty set.

A. The set is the empty set.

A. The set is the empty set.

B. The set is not the empty set.

B. The set is not the empty set.

True
False

True
10 is an element in the set

True
False

False
the “…” means that the sequence carries the same pattern toward and on past the last number
{19,21,23,25,27,29,31,33,35,}
36 is not continued in the pattern

True

False

True
the sequence ends at 8

True
False

True
9 is not even, so it cannot be an element of X

A. There are no cardinal numbers in this set
B. The cardinal number is 5
C.The cardinal number is 7,11,15,19,27

B. The cardinal number is 5

A. The cardinal number of the given set is 1

B. The cardinal number of the given set is 0
C. The cardinal number of the given set is 3

B. The cardinal number of the given set is 0

There are no continents that start with B

A. There are no cardinal numbers in this set
B. The cardinal number is 1
C.The cardinal number is 4

C.The cardinal number is 4

There are 4 letter in the word tank

Are the sets equal?
Are the sets equivalent?

The sets are not equal (they have different elements)

The sets are equivalent (they have the same number of elements)

Are the sets equivalent? explain

A={3,3,3,5,5,7,7,7}

B= {7,5,3}
A. The sets are equivalent because set A does not contain the exact same elements as set B.

B.The sets are not equivalent because set A does not contain the exact same elements as set B.

C.The sets are not equivalent because n(A) ≠ n(B).

D. The sets are equivalent because n(A) = n(B).

D. The sets are equivalent because n(A) = n(B).

For set A to be equivalent to set B means that set A and set B contain the same number of elements. For equivalent sets, n(A) = n(B), that is, the cardinality of set A equals the cardinality of set B.

The cardinality, or the cardinal number, is the number of distinct elements in a set. Repeating elements in a set neither adds new elements to the set nor changes its cardinality.

Are the sets equal? explain

A={3,3,3,5,5,7,7,7}

B= {7,5,3}

A. The sets are not equal because set A contains the exact same elements as set B.

B.The sets are equal because n(A)=n(B).

C.The sets are not equal because

n(A)≠n(B).

D.The sets are equal because set A contains the exact same elements as set B.

D.The sets are equal because set A contains the exact same elements as set B.

The set is infinite.

The set is finite.

The set is infinite.

It is any natural number greater or equal to 1500, since it doesn’t go negative and goes up in value, it is infinite and can go on forever

The set is infinite.

The set is finite.

The set is finite.
The set is finite because natural numbers can’t be negative. Since it is any number below 14,000,000, it will eventually stop at -1

Give an example of two sets that meet the following condition. If the condition is impossible to satisfy, explain why.

The two sets are equivalent but not equal.

The set {x| x∈N and x<5} is {1,2,3,4}. This is equivalent to {2,4,6,8} because both sets have four elements. However, they are not equal because they do not contain the same elements.

A. This is impossible. When 2 sets, A and B, are equivalent, then A=B implies that the two sets are equal, n(A)=n(B)

B. This is impossible. When 2 sets, A and B, are equal, then A=B implies the two sets are equivalent, n(A)=n(B)

C. {1,2,3} and {3,2,1}; {cat, dog, mouse} and {dog, mouse, cat}

B. This is impossible. When 2 sets, A and B, are equal, then A=B implies the two sets are equivalent, n(A)=n(B)

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

$56,000

A. {Engineering}
B. {Social Work, Philosophy, Nursing, Journalism, Marketing, Accounting, Engineering}
C. {Marketing, Accounting, Engineering}
D. {Journalism, Marketing, Accounting, Engineering}

C. {Marketing, Accounting, Engineering}

A. {x| x is a group whose score indicates little or no bias}=Ø

B. {x| x is a group whose score indicates little or no bias}={Group 6, Group 5, Group 1}

C. {x| x is a group whose score indicates little or no bias}={Group 6, Group 5}

D. {x| x is a group whose score indicates little or no bias}={Group 6}

A. {x| x is a group whose score indicates little or no bias}=Ø

A. {x| x is a group whose score indicates moderate bias}={Group 7}

B. {x| x is a group whose score indicates moderate bias}=Ø

C. {x| x is a group whose score indicates moderate bias}={Group 6, Group 3, Group 7}

D. {x| x is a group whose score indicates moderate bias}= {Group 3, Group 7}

A. {x| x is a group whose score indicates moderate bias}={Group 7}

A. {10,14}

B. {9,10,15,16}

C. {9,14}

D. {9,10,14}

A. {10,14}

A. {15}

B. {16}

C. {9,15,16}

D. {11,16}

C. {9,15,16}