Set Theory

Set Theory

​Teacher: Mr. V. Salmon

Objectives

1.      Define the term sets

2.      Identify and give examples of well-defined sets

3.      Identify and list the members of a set

4.      Identify the different types of sets

Match

Match the following

• Fruits

• Classroom Items

• Animals

• Countries

• Planets

Apple

Desk

Dog

Japan

Mars

• Apple

• Desk

• Dog

• Japan

• Mars

Match

Match the following

• Fruits

• Classroom Items

• Planets

• Types of Birds

• Countries

mango

chair

Earth

Eagle

Jamaica

• mango

• chair

• Earth

• Eagle

• Jamaica

What is a Set?

A set is a clearly defined collection of things that has something in common.

For example: Parishes of Jamaica- {St. Mary, St. James, Portland, ...}

A set is made up of members/elements. Therefore all the parishes listed are call the ELEMENTS of the set.

Types of Sets

• ​Empty Set

• Equivalent Set

• Subset

• Disjoint Set

• Complement of a set

• Intersection of a set

• Union of a set

Equal Set

Equal sets have the same number of elements and exactly the same elements. The order in which they appear does not matter.

For example:

A= {1, 2, 3, 4}

B= {4, 3, 2, 1}

Equivalent Set

An equivalent set is a set which has the same number of elements but the elements are not necessarily the same.

For example:

A= {1, 2, 3, 4}

B= {a, b, c, d}

Subset

A subset is a set contained in the given set. Every element of the subset is an element of the given set. (A is a subset of B)

Disjoint Set

Disjoint sets have no common element

Complement of a set

The complement of a given set, is the set of all elements in its universal set that does not belong to the given set.

Intersection of a set

The intersection of two sets A and B, is the set of all elements common to both A and B.

Union of a set

The union of two sets A and B is the set of all elements which belong to either A or B, or both A and B.

Venn Diagram

Multiple Choice

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

• {3, 5, 7}

• {2, 3, 5, 7}

• {2, 3, 5, 7, 9}

• {1, 2, 3, 5, 7, 9}

Multiple Choice

What does this symbol ( ∪ ) represent in set theory?

• Union

• Intersection

• Disjointed

• Subset

Multiple Choice

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?

• {3, 5, 7}

• {2, 3, 5, 7}

• {2, 3, 5, 7, 9}

• {1, 2, 3, 5, 7, 9}

Multiple Choice

Find n(A) for the set:
A = {14, 16, 18, 20, 22, 24}

• 6

• 12

• 4

• 8

Multiple Choice

If

U (the universal set) = {1, 3, 5, 7, 9, 11, 13, 15, 17} and W = {5, 7, 9, 11}, then W' = . . ..

• {1, 3, 13, 15, 17}

• {1, 3}

• {2, 4, 6, 8, 10, 12, 14, 16}

• {1, 3, 5, 7, 9, 11, 13, 15, 17}

Multiple Choice

What statement does the shaded region represent

• A or B

• Not A

• A and B

• Not B

Multiple Choice

What does this symbol ( ∩ ) represent in set theory?

• Union

• Intersection

• Disjointed

• Subset

Multiple Choice

What type of set is denoted as either { } or ∅?

• Universal Set

• Empty (or Null) Set

• Disjointed Set

• Complement of a Set

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Multiple Choice

How many senior boys play football and wrestle?

• 9

• 12

• 18

• 39

Multiple Choice

How many senior boys play football but do not wrestle?

• 9

• 12

• 18

• 104

Multiple Choice

How many senior boys play football or wrestle?

• 9

• 21

• 30

• 39

Multiple Choice

How many people own cats?

• 3

• 4

• 6

• 7

• 10

Multiple Choice

How many people ONLY own dogs?

• 3

• 4

• 6

• 7

• 9

Multiple Choice

Equal sets have

• the exact same elements

• the same number of elements

• the opposite

• nothing

Multiple Choice

Equivalent sets have

• the opposite elements

• nothing

• the exact same elements

• the same number of elements

Multiple Choice

Left Pocket (L) = {pencils, erasers, pens}
Right Pocket (R) = {gloves, paper, coins, phone}
What is L ∪ R?

• ∅

• {pencils, erasers, pens}

• {gloves, paper, coins, phone}

• {pencils, erasers, pens, gloves, paper, coins, phone}

Multiple Choice

What does this symbol ( ∩ ) represent in set theory?

• Union

• Intersection

• Disjointed

• Subset

Multiple Choice

If A={6,8,10,12} then 5 ∈ A

• True

• False

Multiple Select

The objects in the set are called its

• items

• members

• elements

• objects

Multiple Choice

If A = {1, 2, 3, 4, 5, 6} and B = {1, 2, 3, 5, 7, 9} What is A ⋂ B?

• {1, 2, 3, 4, 5, 6, 7, 9}

• {1, 2, 3, 5}

• {4, 6, 7, 9}

• { }

Multiple Choice

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

• {3, 5, 7}

• {2, 3, 5, 7}

• {2, 3, 5, 7, 9}

• {1, 2, 3, 5, 7, 9}

Multiple Choice

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

• {-4, -3, -2, -1, 0, 1, 2, 3}

• {-3, -2, -1, 1, 2, 3}

• {-4, -3, -2, -1, 1, 2, 3, 4}

• {-4, -3, -2, -1, 1, 2, 3}