Introduction to Set Theory

Introduction To Set Theory

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Lesson objective

Define a Set and Write a Set Using Different Ways.

There are three common ways to designate sets:

• The list or roster method

• The descriptive method

• Set-Builder Notation

Multiple Choice

A ............................................ : is a collection of objects. A = { 1, 2, 3, … }.

• Set

• Element

• Variable

• Cardinality

Multiple Choice

A ............................................ : Each object in a set.

• Set

• Element

• Variable

• Cardinality

Multiple Choice

One method of designating a set, in which elements are listed between braces, with commas between the elements. The order in which we list elements isn’t important. Name sets by using a capital letter.

A = { 1, 2, 3, … }.

• Roster Method

• Descriptive Method

• Set-Builder Notation

Multiple Choice

One method of designating a set, in which we use a short verbal statement to describe the set.

• Roster Method

• Descriptive Method

• Set-Builder Notation

Multiple Choice

One method of designating a set, in which we use variables, braces and a vertical bar | that is read as “such that.”.

A = { x | x ∈ N and x < 7 }

• Roster Method

• Descriptive Method

• Set-Builder Notation

Fill in the Blanks

Write the set of months that end with the letter y in the English language.

Multiple Choice

Decide whether the statement is True or False.

21 ∈ {2, 5, 8, 11, ... }.

• True

• False

Multiple Choice

Decide whether the statement is True or False.

map ∉ {m, a, p}.

• True

• False

Multiple Select

N = {1, 2, 3, 4, … }

• Natural Numbers

• Counting Numbers

• EVEN Natural Numbers

• Odd Natural Numbers

Multiple Choice

E = {2, 4, 6, 8, … }

• Natural Numbers,

  Counting Numbers

• EVEN Natural Numbers

• Odd Natural Numbers

Multiple Choice

O = {1, 3, 5, 7, … }

• Natural Numbers,

  Counting Numbers

• EVEN Natural Numbers

• Odd Natural Numbers

Fill in the Blanks

Write the set, using the roster method.

The set of even natural numbers from 80 to 90.

Fill in the Blanks

Write the set, using the roster method.

The set of odd natural numbers greater than 10 and less than 20.

Fill in the Blanks

Write the set, using the roster method.

The set of integers from -3 to 3.

Multiple Choice

A ............................................ :

is a symbol (usually a letter) that can represent different elements of a set.

• Set

• Element

• Cardinality

• variable

Fill in the Blanks

Write the set, using the roster method.

K = { x | x ∈ E, x > 9, and x < 19}

Fill in the Blanks

Designate the set with elements 11, 13, 15, 17, . . . using the roster method.

Fill in the Blanks

Using the roster method, write the set of odd natural numbers between 50 and 55.

Fill in the Blanks

Write the set, using the roster method.

B = { x | x ∈ E and 15 < x < 31}

Multiple Choice

............................................ :

A set with no elements.

• Set

• Well-Defined Set

• Finite Set

• Infinite Set

• Empty Set, Null set, { }, ∅

Multiple Select

Which of the following sets are empty?

• { x | x is a natural number divisible by 7}

• { x | x is a human being living on Mars}

• {{ }}

• The set Z consists of the living people on Earth who are over 120 years old.

Multiple Select

............................................ :

is the number of elements in the set.

• variable

• Cardinality

• Cardinal Number

• One-To-One Correspondence

Multiple Choice

Find the cardinal number of the set.

A = {z, y, x, w, v}

• 1

• 2

• 3

• 4

• 5

Multiple Choice

Find the cardinal number of the set.

B = { x | x ∈ E and 15 < x < 31}

• 5

• 6

• 7

• 8

• 9

Multiple Choice

Find the cardinal number of the set.

C = {Chevrolet}

• 9

• 8

• 7

• 6

• 1

Multiple Choice

............................................ :

A set that has no elements, or has cardinality that is a natural number.

• Well-Defined Set

• Empty Set

• Null set

• Finite Set

• Infinite Set

Multiple Choice

............................................ :

A set that is not finite. It has an unlimited number of elements.

• Well-Defined Set

• Empty Set

• Null set

• Finite Set

• Infinite Set

Multiple Choice

Classify the set as Finite or Infinite.

Set P is the set of numbers that are multiples of 6.

• Finite

• Infinite

Multiple Choice

Classify the set as Finite or Infinite.

{ x | x is a member of the UAE Army}.

• Finite

• Infinite

Multiple Choice

Classify the set as Finite or Infinite.

{3, 6, 9, ... , 24}.

• Finite

• Infinite

Multiple Choice

Classify the set as Finite or Infinite.

The set of all possible computer passwords.

• Finite

• Infinite

Multiple Choice

............................................ :

If they have exactly the same members or elements.

• Empty Set, Null set

• Finite Set

• Infinite Set

• Equal Sets A = B

• Equivalent Sets A ≅ B

Multiple Choice

............................................ :

If they have the same number of elements, that is, n (A) = n (B).

• Empty Set, Null set

• Finite Set

• Infinite Set

• Equal Sets A = B

• Equivalent Sets A ≅ B

Multiple Select

State whether each pair of sets is Equal, Equivalent, or Neither.

{d, o, g}; {c, a, t}

• Equal

• Equivalent

• Neither

Multiple Select

State whether each pair of sets is Equal, Equivalent, or Neither.

{run}; {r, u, n}

• Equal

• Equivalent

• Neither

Multiple Select

State whether each pair of sets is Equal, Equivalent, or Neither.

{t, o, p}; {p, o, t}

• Equal

• Equivalent

• Neither

Multiple Select

State whether each pair of sets is Equal, Equivalent, or Neither.

{10, 20, 30}; {1, 3, 5}

• Equal

• Equivalent

• Neither

Multiple Choice

............................................ :

If each element in the first set can be paired with exactly one element of the second set and each element of the second set can be paired with exactly one element of the first set.

• Well-Defined Set

• One-To-One Correspondence

• Cardinality

• Equivalent

Multiple Choice

Decide whether the statement is True or False.

The sets {North, South, East, West} and {sun, rain, snow, sleet} have a one-to-one correspondence.

• True

• False

Multiple Choice

Are you confident about our lesson Today?

• Very Confident

• Somewhat Confident

• Little Confident

• Not Confident

The End

Thank You :)