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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
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”.
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.
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.

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 (...)

the set of counting numbers

the set of integers
Null Set
it is Denoted by ___ or {}.
A set that has no elements

the set of mangoes growing in a coconut tree.
the set of airconditioners in the room.
Unit Set
– A set with one element

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.

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.

the set of counting numbers.

the set of bachelor courses in Riverside
Describing Sets
roster method

rule method
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.
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.
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.
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.
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


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