Basic Concepts on Sets and Set Operations

Basic Concepts on Sets and Set Operations

Multiple Choice

Which one does not belong to the group?

A Set

is a well-defined group of distinct objects that share a common characteristic. The objects in a set are called elements or members of the set.

A group is well-defined set

when one can be certain whether an object is a part of the set or not. This means it is not free to different interpretation when viewed or judged by different people.

A group is not-defined set

when one cannot be certain whether an object is a part of the set or not. This means it is free to different interpretation when viewed or judged by different people.

Quiz

Write S if the given is a well-defined set or NS if not.

Fill in the Blanks

pretty students in your school

pretty students in your school

It is not a set, because it is not well-defined. A student may be pretty for one but not for another. Also, we are not given the criteria to determine if a student is pretty.

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counting number less than 8

counting number less than 8

It is a set. Counting numbers less than 8 is N = {1, 2, 3, 4, 5, 6, 7}.

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True or False? Well-defined means specific.

Ways of Describing Sets

A. Roster Method or

Listing Method

B. Word Description

C. Set Builder Notation

or Rule Method

Multiple Choice

A ________ is a set in which it is possible to list and count all the members of the set.

• finite set

• infinite set

Multiple Choice

A ________ is a set in which it is not possible to list and count all the members of the set.

• finite set

• infinite set

More about Sets

Cardinality of a Set

Empty Set or Null Set

Equal and Equivalent Sets

Universal Set

Subsets and Proper Subsets

Given: E = {even numbers}

Answer the given questions

Fill in the Blanks

Given: E = {even numbers}

Is there an element of the set? Yes or no?

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Given: E = {even numbers}

If yes, how many elements are there?

Cardinality of a finite set

is the number of distinct elements in the set.

Example: Find the cardinality of the following set

D = {weekdays}

n(D) = 5

The elements are: Monday, Tuesday, Wed., Thurs., and Friday

Empty Set or Null Set

A set without elements is called an empty set or a null set and is denoted by { }.

Equal and Equivalent Sets

• Two sets A and B are equal if they have exactly the same elements.

• Two sets A and B are equivalent if they have the same number of elements (cardinality).

Universal set or universe

is the set that contains all objects under consideration.

Subsets and Proper Subsets

• A is a subset of B, if and only if every element of A is also an element of B.
• A is a proper subset of B, if and only if every element of A is also an element of B, and A is not equal to B.

Quiz

type in small letter onyl your answers

Fill in the Blanks

A collection well-defined objects, things, or symbols that share common characteristics.

Fill in the Blanks

These are the objects, things, or symbols in the set.

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Part of a set or the set itself.

Fill in the Blanks

The set having no elements.

Fill in the Blanks

The number of elements of a given set.

Questions?

Check you virtual classroom for the assignments.