Sets-A WELL DEFINED COLLECTION OF OBJECTS : Sets-A WELL DEFINED COLLECTION OF OBJECTS
Slide 2 : Submitted by
ADITYA Padmanabhan
Slide 3 : ROSTER AND SET-BUILDER
EMPTY EQUAL INFINITE AND FINITE SETS
SUBSETS, POWER SET, UNIVERSAL SET
INTERVALS
OPERATIONS ON SETS
DIFFERENCE OF SETS
COMPLEMENT OF A SET
SUMMARY
ROSTER AND SET-BUILDER : ROSTER AND SET-BUILDER In roster form, all the elements of a set are lisetd, the elements are being seperated by commas and are closed within braces{}.
In set-builder form, all the elements of a set possess by any element outside the set.
EMPTY, eQual, infinite and finite sets : EMPTY, eQual, infinite and finite sets A set which does not contain any element is called empty set or void set.
Two sets A and B are said to be equal if they have exactly the same elements and we write a=b. Otherwise is not =.
A set which is empty or consists of a definite no: of elements is finite otherwise, called infinite.
SUBSETS, POWER SET, UNIVERSAL SET : SUBSETS, POWER SET, UNIVERSAL SET A set A is said to be a subset of a set B if every element of A is also an element of B.
The collection of all the subsets of a set is a power set.
All the subsets and the set itself is a universal set.
INTERVALS : INTERVALS closed interval:- [a,b].
Open interval:- (a, b)
Open-closed:- (a.b]
Closed-open:- [a,b)
OPERATIONS ON SETS : OPERATIONS ON SETS Union:- the union of the set A and B which consists of all the elements of A and B.
A B = B A
(A B) C= A (B C)
A Φ=A
A A=A
U A=U
Intersection:- the intersection of sets A and B is the set of all elements which are common to both A and B.
THE LAWS ARE VICE-VERSA OF UNION FOR INTERSECTION = UNION
DIFFERENCE OF SETS : DIFFERENCE OF SETS The difference of sets A and B is the set of elements which belong to A but not B. COMPLEMENT OF A SET Let U be the universal set and A a subset of U. then the complement of A is the set of all elements of U which are not the elements of A. A’ IS THE COMPLEMENT OF A.
DE MORGAN’S LAW
(A B)’=A’ B’
(A B)’=A’ B’
SUMMARY : SUMMARY (A’)’=A
Φ’=U
U’= Φ
A-B=elements in a not in B
P(A)=power set OF A
SUBSETS CAN BE FOUND OUT BY 2n
Subset of (a,b)= Φ,{a},{ b},{ a,b}
THE END : THE END