Download - Sets final
Compiled by
Prof . Sandeep Gupta
SETS
Meaning Set is a WELL DEFINED collection of objects
Meaning
MeaningBag is a set which consists of well
definedObjects i.e. pencils, erasers, scale,books etc. These objects are the
elements ofthis set
Examples
ExamplesCan a beautiful girl or group of beautiful girls
bea set?
ExamplesThe answer is ‘NO’ because beauty is not well defined
ExamplesCan a group of boys be a collection of Set?
‘YES’ , group of boys is a set because numberof boys in the group are well defined
Ur turn to think…..
A smart man …. Is it a Set?
Ans. ………
ExamplesGroup of good teachers in school…….is it acollection of set?
Ans………
ExamplesCollection of prime numbers?
Ans…….
SETSIndiviual object in the set is called ELEMENT
or a MEMBER of the set.Sets are denoted by capital alphabets , e.g. A,
B, C etc.Elements of set are denoted by small
alphabets , e.g. a, b, c etc.If a is an element of set X then we write it as
a Є XIf a is not an element of set X, then it is
written as a Є X
Types of Sets
Types of
sets
empty set
Singeltonset
Finiteset
Infiniteset
Types of SetsEmpty set : it’s a set having no element. Also
known as Null set, it is denoted by ФSingleton set : it’s a set having only one elementFinite set : it’s a set wherein counting of
elements ends at a certain stageInfinite set : it’s a set in which counting of
elements do not end at any stageAn empty set is a finite setNatural and whole numbers, integers, rational
and real numbers are infinite sets
Few concepts worth rememberingNatural and Whole numbers these includes numbers like 1,2,3,4 etconly difference is we include ‘0’ (zero) in
whole numbers but not in natural numbersare not fractions, decimals or negative
numbersIntegers are positive or negative numbers and
includes zeroare whole numbers but can be negative too
Few concepts worth rememberingRational numbers Includes integers, fractions and repeating
decimals• Irrational numbers Includes only decimals that have no pattern and
continue forever• Real numbers It includes every thing discussed above
SymbolsSymbols commonly used:Whole numbers WIntegers IRational numbersQNatural numbers NReal numbers R
Methods of writing setsListing method (Roster form)Rule method (Set builder form)Examples
1. Set of first 20 even natural numbersRoster formA = {2, 4, 6, 8, ………40}Set builder formA = {x|x is even natural number, 2 ≤ x ≤
40}
ExamplesExample 2Set of first 10 multiples of 5Roster formA = {5, 10, 15, 20, …..50}Set builder form
A = {x|x=5n, n Є N, 1 ≤ n ≤ 10}
Concept of SubsetsIf every element of set B is an element of set
A, then set B is subset of set ASubset can be proper subset or improper
subsetIf set B is subset of set A and set A contains
at least one element which is not in set B, then set B is proper subset of set A
If set A is subset of set B and if set B is subset of set A, then they are improper subsets of each other
B A is to be read as set B is proper subset of set A
Concepts of subsetsA B is to be read as set A is super set
of set BA B is to be read as set A is improper
subset of set BEvery set is subset of itselfEmpty set is subset of every set
Universal setA non-empty set of which all the sets under
consideration are the subsets of that set is called universal set
It is denoted by ‘U’
The End