**Set and Basic Notation**

Sets

It is a collection of object of any sort.

It is a group of distinct objects.

Examples of sets

The set of freshman students in Math 17.

The set of all points that lie on a given line.

The set if distinct letters in the word “Mississippi”.

Element

it is an object belongs to the set or a subset of the set.

the symbol, , is used to the membership of an element of object to a set.

Capital letters are usually used to denote the set.

Illustration

If we denote the distinct letters Mississippi as M,

then s M,

but t M.

Finite Set

If the set has a definite number of elements.

example:

the set of Philippine presidents.

the set of vowels in an English alphabet.

Infinite set

If the set has unlimited number of elemets. It is

usually denoted by (...)

example:

the set of counting numbers

the set of integers

Null Set

it is Denoted by ___ or {}.

A set that has no elements

•

examples:

the set of mangoes growing in a coconut tree.

the set of airconditioners in the room.

Unit Set

– A set with one element

examples:

the set of teachers inside the classroom.

the set of wives in a family.

Types of sets

finite set

infinite set

null set

unit set

Roster Method

This method lists the number of elements in a set.

example:

the set of counting numbers.

the set of bachelor courses in Riverside.

Rule method

We may indicate a set by enclosing in braces a descriptive phrase.

example:

the set of counting numbers.

the set of bachelor courses in Riverside

Describing Sets

roster method

rule method

SUBSETS

The set A is said to be a subset of B, if every

element of A is found on B.

It is denoted by ___.

Universal Set

-Denoted by U.

it contains all the elements of its subsets.

Example

A = { a, b }

B = { 1, 2, 3 }

Relationships between sets

Two sets C and D are equivalent, C D, if there exists a one-to-one correspondence between their elements.

Relationships between sets

Relationships can be describe using a Venn Diagram.

A Venn diagram is a diagram with one or more circles or closed regions representing sets.

Complement

Consider C as any subset of a universal set U.

the complement of set C, denoted by C’, is the set whose elements are in U but not in C.

Union

consider the to sets C and D.

the union of C and D, denoted by C U D, is the set whose elements belong to either C or D.

Intersection

Consider the sets C and D. the intersection of the sets C and D, denoted by C __ D, is the set whose elements belong to both C and D.

Basic Operations of Sets

complement

union

intersection

Examples:

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

A = { 2, 4, 6, 8, 10 }

B = {1, 3, 5, 6, 7, 9}