Sets and Problems Involving Sets

Multiple Choice

Which of the following is a well-defined set?

• A set of beautiful sceneries

• A set of good basketball players

• A set of Philippine Presidents

• A set of successful leaders

Multiple Choice

List all the letters in the word “school”.

• {s, c, h, o, o, l}

• {s, c, h, o, l}

• {s, h, o, o, l}

• {s, c, o, l}

Multiple Choice

Which of the following is the symbol of an empty set?

• ∩

• U

• ⊆

• ∅

Multiple Choice

Let A = {1, 2, 3, 4, 5, 6} , B = {2, 4, 5, 6}

Find A U B

• {1, 2, 3, 4, 5, 6}

• {2, 4, 5, 6}

• {2, 4, 6}

• {1, 3, 5}

Multiple Choice

Let A = {1, 2, 3, 4, 5, 6} , B = {2, 4, 5, 6}

Find A ∩ B

• {1, 2, 3, 4, 5, 6}

• {2, 4, 5, 6}

• {2, 4, 6}

• {1, 3, 5}

Multiple Choice

A survey was conducted among 50 people on the ice cream flavor they liked. It was found out that 28 liked chocolate, 15 liked mango, and 20 liked strawberr. Furthermore, 8 liked chocolate and strawberry, and 7 liked chocolate and mango, and 4 liked all the 3 flavors.

How many people liked Chocolate only?

• 28

• 17

• 8

• 7

Multiple Choice

A survey was conducted among 50 people on the ice cream flavor they liked. It was found out that 28 liked chocolate, 15 liked mango, and 20 liked strawberr. Furthermore, 8 liked chocolate and strawberry, and 7 liked chocolate and mango, and 4 liked all the 3 flavors.

How many people liked mango only?

• 15

• 14

• 7

• 1

Multiple Choice

A survey was conducted among 50 people on the ice cream flavor they liked. It was found out that 28 liked chocolate, 15 liked mango, and 20 liked strawberr. Furthermore, 8 liked chocolate and strawberry, and 7 liked chocolate and mango, and 4 liked all the 3 flavors.

How many people liked strawberry only?

• 20

• 8

• 5

• 4

Multiple Choice

A survey was conducted among 50 people on the ice cream flavor they liked. It was found out that 28 liked chocolate, 15 liked mango, and 20 liked strawberr. Furthermore, 8 liked chocolate and strawberry, and 7 liked chocolate and mango, and 4 liked all the 3 flavors.

How many people liked all the three flavors?

• 3

• 4

• 7

• 9

Multiple Choice

A survey was conducted among 50 people on the ice cream flavor they liked. It was found out that 28 liked chocolate, 15 liked mango, and 20 liked strawberr. Furthermore, 8 liked chocolate and strawberry, and 7 liked chocolate and mango, and 4 liked all the 3 flavors.

How many people did not like the three flavors at all?

• 3

• 4

• 7

• 9

Fill in the Blanks

Why did you group the object as such?

Fill in the Blanks

How many groups are there?

Fill in the Blanks

What are the names of the groups created?

Multiple Choice

In the collections of objects below, which does not belong to the group?

Multiple Choice

The set of young politicians

• Well-defined

• Not

Multiple Choice

The set of types of matter

• Well-defined

• Not

Multiple Choice

The set of versatile actresses.

• Well-defined

• Not

Multiple Choice

The set of all oceans of the earth.

• Well-defined

• Not

Multiple Choice

The set of months containing 31 days.

• Well-defined

• Not

Multiple Choice

The objects contained in the set.

• capital letters

• set

• ellipsis

• { }

• Elements

Multiple Choice

A well-defined group or collection of objects that share common characteristics.

• capital letters

• set

• ellipsis

• { }

• Elements

Multiple Choice

It is represented by three dots which is use to indicate that a set has many / infinite elements.

• capital letters

• set

• ellipsis

• { }

• Elements

Multiple Choice

A symbol use to group the elements of a set.

• capital letters

• set

• ellipsis

• { }

• Elements

Multiple Choice

A symbol used in represent a set.

• capital letters

• set

• ellipsis

• { }

• Elements

Multiple Choice

Which of the following is the set of animals living in water?

• A = {dolphin, whale, milk fish}

• B = {lion, buffalo, deer}

• C = {duck, chicken, turkey}

• D = {eagle, parrot, dove}

Multiple Choice

Given: A = {b, i, o, d, e, g, r, a, d, a, b, l, e}, which of the following is INCORRECT?

• It uses capital letter to name set.

• It does not list the object once.

• It uses braces.

• It uses commas.

Multiple Choice

The set of provinces in Region 12.

• E = {Aklan, Antique, Capiz, Guimaras, Ilo-ilo, Negros Occidental}

• . F = {South Cotabato, North Cotabato, Sultan Kudarat, Sarangani, General Santos}

• G = {Ilocos Norte, Ilocos Sur, La Union, Pangasinan}

• H = {Cavite, Laguna, Batangas, Rizal, Quezon}

Multiple Choice

The set of months containing 30 days

• I = {January, March, May}

• J = {February, April, June}

• K = {June, July, August}

• June, September, November}

Multiple Choice

The set of secondary colors.

• M = {red, green, yellow}

• N = {brown, pink, blue}

• O = {green, orange, violet}

• P = {white, black, grey}

Multiple Choice

The set of all even numbers from 2 to 10

• well-defined

• NOT

Multiple Choice

The set of all factors of 18.

• well-defined

• NOT

Multiple Choice

The set of responsible citizens.

• well-defined

• NOT

Multiple Choice

The set of letters in the word “FATHER”.

• well-defined

• NOT

Multiple Choice

The set of hardworking front liners.

• well-defined

• NOT

Multiple Choice

Given: A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Find: The set of odd numbers.

• {0,1,2,3,4,5}

• {1,3,5,7,9}

• {2,4,6,8,10}

• {6,7,8,9,10}

Multiple Choice

Given: A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Find: The set of all factors of 10

• {1,10,2,5}

• {1,10,2,3}

• {1,10,2,0}

• {1.10.2.1}

Multiple Choice

Given: A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Find: The set of multiples of 4.

• {2,4}

• {4,6}

• {4,8}

• {4,10}

Multiple Choice

Given: A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Find: The set of negative integers.

• {2,4}

• {4,6}

• {4,8}

• {∅}

Fill in the Blanks

Set B is the set of letters in the word “recognition”.

Fill in the Blanks

Set C is the set of even numbers less than 2.

Fill in the Blanks

Set D is the set of odd numbers between 3 and 9.

Fill in the Blanks

Set E is the set of factors of 12.

Multiple Choice

A set with no element is an empty set or

• universal set

• null set

• subset

• { } or ∅

• cardinality of set

Multiple Choice

The number of elements in the set refers to

• universal set

• null set

• subset

• { } or ∅

• cardinality of set

Multiple Choice

The U is the set that contains all objects under consideration.

• universal set

• null set

• subset

• { } or ∅

• cardinality of set

Multiple Choice

If every element in A is also an element in B, then A is a _________________ of B.

• universal set

• null set

• subset

• { } or ∅

• cardinality of set

Multiple Choice

The symbol for empty set or null set is ___________________.

• universal set

• null set

• subset

• { } or ∅

• cardinality of set

Multiple Choice

S = {0, 1, 2, 3, 4, …, 10}

O = {d, a, y}

L = {3, 6, 9, 12}

V = {5, 10, 15, 20, 25}

I = {r, o, s, e}

N = {roots, stem, leaves, flowers, fruits}

G = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

The cardinality of Set G is 8.

• TRUE

• FALSE

Multiple Choice

S = {0, 1, 2, 3, 4, …, 10}

O = {d, a, y}

L = {3, 6, 9, 12}

V = {5, 10, 15, 20, 25}

I = {r, o, s, e}

N = {roots, stem, leaves, flowers, fruits}

G = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

{5, 15, 25} is a subset of Set V

• TRUE

• FALSE

Multiple Choice

S = {0, 1, 2, 3, 4, …, 10}

O = {d, a, y}

L = {3, 6, 9, 12}

V = {5, 10, 15, 20, 25}

I = {r, o, s, e}

N = {roots, stem, leaves, flowers, fruits}

G = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

{8} is a subset of Set L.

• TRUE

• FALSE

Multiple Choice

S = {0, 1, 2, 3, 4, …, 10}

O = {d, a, y}

L = {3, 6, 9, 12}

V = {5, 10, 15, 20, 25}

I = {r, o, s, e}

N = {roots, stem, leaves, flowers, fruits}

G = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

The cardinality of Set O is 7is a subset of Set L.

• TRUE

• FALSE

Multiple Choice

S = {0, 1, 2, 3, 4, …, 10}

O = {d, a, y}

L = {3, 6, 9, 12}

V = {5, 10, 15, 20, 25}

I = {r, o, s, e}

N = {roots, stem, leaves, flowers, fruits}

G = {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

The number of elements in Set N is 5.

• TRUE

• FALSE

Multiple Choice

Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The universal set is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

• TRUE

• FALSE

Multiple Choice

Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

{2, 4, 6, 8, 10} is a subset of U.

• TRUE

• FALSE

Multiple Choice

Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

{0, 10} is a subset of U.

• TRUE

• FALSE

Multiple Choice

Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Empty set { } is a subset of U.

• TRUE

• FALSE

Multiple Choice

Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The cardinality number of set U is 10

• TRUE

• FALSE

Multiple Select

What animals can live on land?

• dog

• frog

• cow

• cat

• fish

Multiple Select

What animals can live in water?

• dog

• frog

• cow

• cat

• fish

Multiple Select

What animals can live both in land and water?

• dog

• frog

• cow

• cat

• fish

Fill in the Blanks

Given: A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B = {2, 4, 6, 8, 10} C = {1, 3, 5, 7, 9}

A ∩ C =

Fill in the Blanks

Given: A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B = {2, 4, 6, 8, 10} C = {1, 3, 5, 7, 9}

A 𝖴 B =

Fill in the Blanks

Given: A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B = {2, 4, 6, 8, 10} C = {1, 3, 5, 7, 9}

A – C

Fill in the Blanks

The

of sets A and B, written as A 𝖴 B, is the set of elements that are members of A, or members of B, or members of both A and B.

Fill in the Blanks

The

of two sets A and B, written as A ∩ B, is the set of all elements common to both sets A and B.

Fill in the Blanks

The

of set A and B, written as A – B, is a set of elements in A that are not in B.

Fill in the Blanks

If A = {a, b, c, d, e} and B = {a, c, f, g, h, i},

find: A 𝖴 B

Fill in the Blanks

If A = {a, b, c, d, e} and B = {a, c, f, g, h, i},

find: A ∩ B

Fill in the Blanks

If A = {a, b, c, d, e} and B = {a, c, f, g, h, i},

find: A - B

Fill in the Blanks

How many had ridden the bus only?

Fill in the Blanks

How many had ridden the LRT only?

Fill in the Blanks

How many had ridden the jeep only?

Fill in the Blanks

How many did not ride on any of the three modes of transportation?

Fill in the Blanks

How many liked eating both in Restaurant A and Restaurant B?

Fill in the Blanks

How many liked eating In Restaurant A only?

Fill in the Blanks

How many liked eating In Restaurant B only?

Multiple Choice

Which of the following is a well-defined set?

• A set of good writers

• A set of factors of 3

• A set of honest students in grade seven

• A set small numbers

Multiple Choice

Which of the following is the symbol of a null set?

• Ս

• ∩

• ⊆

• ∅

Multiple Choice

Michelle listed the set of all letters in the word “serendipity” as shown below. What is wrong with this set? A = {s, e, r, e, n, d, i, p, i, t, y}

• It uses commas.

• It uses braces.

• The objects in this set are not listed once.

• A capital letter is used to represent this set.

Multiple Choice

Given the set of letters in the word “LOVE”. What is the cardinality of the givenset?

• 11

• 8

• 6

• 4

Multiple Choice

What is the cardinality of {10, 20, 30, …, 80}?

• 8

• 10

• 12

• 14

Fill in the Blanks

The 150 Grade 7 students participated in school’s Math Olympics. 64 students registered in Math Trail, 78 students registered in Amazing Race and 28 students registered in both Math Trail and Amazing Race.

a. How many students registered in Math Trail only?

Fill in the Blanks

The 150 Grade 7 students participated in school’s Math Olympics. 64 students registered in Math Trail, 78 students registered in Amazing Race and 28 students registered in both Math Trail and Amazing Race.

b. How many students registered in Amazing Race only?

Fill in the Blanks

The 150 Grade 7 students participated in school’s Math Olympics. 64 students registered in Math Trail, 78 students registered in Amazing Race and 28 students registered in both Math Trail and Amazing Race.

c. Are there students who did not registered in both events, how many?

Fill in the Blanks

Find how may had taken Math only?

Fill in the Blanks

Find how may had taken English only?

Fill in the Blanks

Find how may had taken Science only?

Fill in the Blanks

How many students had been considered in a survey?