Set Notation
Set Notation
 Sets are collections of unique objects known as elements.
 The notation
{a, b, c}
signifies a set with elements ‘a’, ‘b’ and ‘c’.  The order of elements in a set is not significant.
{a, b}
is the same as{b, a}
.
Empty and Universal Sets
 An empty set or null set is a set with no elements, denoted as
{}
or∅
.  A universal set contains all elements under consideration, usually denoted by the symbol
U
.
Membership and Inclusion
 If ‘a’ is an element of a set
A
, we writea ∈ A
. If ‘a’ is not an element ofA
, we writea ∉ A
.  Inclusion refers to all elements of one set being within another set. If every element in set A is also in set B, we write
A ⊆ B
. A = B
signifies that sets A and B are identical: every element of A is in B and every element of B is in A.
Cardinality

The Cardinality of a set is the number of elements in the set, denoted as A . For example, if A = {a, b, c}
, thenA = 3.
Set Operations
 Union of two sets
A
andB
, denoted asA ∪ B
, is a set containing all elements of A and B.  Intersection of
A
andB
, denoted asA ∩ B
, is a set containing common elements of A and B.  Difference of
A
fromB
, denoted asA \ B
, is a set of elements in A but not in B.  Complement of a set
A
, denoted asA'
orA̅
, refers to all elements not in A but in the universal set U.
Cartesian Products
 Cartesian Product of two sets
A
andB
, denoted asA × B
, is a set of all ordered pairs(a, b)
wherea
belongs toA
andb
belongs toB
. The order of elements does matter in Cartesian product.
Venn Diagrams
 Venn Diagrams are graphical representations of sets and their relations, wherein each set is represented with a circle or oval and elements are represented as points within the shapes. Intersection of sets is visually depicted as overlapping areas.