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Set and Basic Notation

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Gabby Zaragoza

on 16 June 2014

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Transcript of Set and Basic Notation

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}
Full transcript