SETS
Empty Set (null set):
A set is a collection of well-defined objects called elements.
some denotations
Finite – Infinite sets
UNIVERSAL SET (U)
SUBSETS
Georg Cantor is the first mathematician who uses the “SET CONCEPT” in mathematics. 
Sets are denoted by capital letters, such as A, B, C....
x
A
n(A)
x
A
Representation of Sets
- Venn diagram
- Listed form
- Set-builder form
Elements of sets are written inside of the set brackets { } by putting comma between two elements.
Elements of a set are written in a simple closed shape.
The set that contains all the elements being discussed is called universal set, and it is denoted by U.
A set which contains no element is called empty set denoted by symbol { } or
A = {1, 3, 5, 7, 9, 11}
N = { 0 , 1 , 2 , 3 , 4, ... }
Equal Sets:
A=B;
A⊆ B
AB={xxA xB }
Properties of subsets
b) The empty set is a subset of any set. That is Ø.......A.
c) Every set is a subset of itself , that is for any set A , A.....A.
a) Every set is a subset of universal set , that is for any set A , A .....U.
d) If A⊂B and B⊂C then A....C
e) If A⊂B and B⊂A then A ......B.
Number of subsets
2n(A) – 1 = 2k – 1
2
n(A)=2k
OPERATIONS ON SETS
UNION OF SETS
Remark
INTERSECTION OF SETS
The properties of Union and Intersection
c) Associative Property
d) Distributive property
b) Commutative Property
e) Subset property
a) Idempotent property
DIFFERENCE OF TWO SETS
The difference of the sets A and B is the set of elements of A which does not belong to B, and it is
denoted by A−B or A\B.
COMPLEMENT OF A SET
Properties of Complement:
De Morgan’s Law
Common Properties of Complement and Difference of the Sets
SET PROBLEMS
data for set problems
ordered pairs
CARTESIAN PRODUCT (Cross Product)