Set
A set is a well-defined collection of distinct objects.
eg: A= {a, e, i, o, u}
B= {2,4,6,8,10}
Methods of representing a set
1. Listed method: In this method, all the elements of set are
within curly brackets.
eg: A= {a, e, i, o, u}
2. Descriptive method: In this method, a set is represented
by describing its elements in words.
eg: A= {set of vowel letters}
3. Set builder method: In this method, a set is represented
by stating the common property of its elements using a
variable.
eg: A= {x/x ∈ N ∧ x ≤ 10}
Types of sets
1. Universal set (U): It is the set that contains all the
elements under discussion.
Eg: U = {1,2,3,4,5,6,7,8,9,10}
2. Overlapping set: Two sets having one or more common
elements are called overlapping sets.
Eg: A= {1,2,3}
B= {3,4,5}
Here, common element =3
3. Disjoint set: Two sets having no common elements are
called disjoint sets.
Eg: A= {1,2,3}
B= {4,5,6}
A∩B= ∅
4. Subset (⊆): A set ‘A’ is called a subset of set B if every
element of A is also an element of B.
Eg: A = {2,4}
B = {2,4,6,8}
Here, A⊆B
a. Proper set: It is a subset that is not equal to original
set.
Eg: A= {2,4}
B = {2,4,6,8}
Here, A⊂ B
b. Improper set: A set is an improper subset of itself.
Eg: A = {1,2,3}
B = {1,2,3}
Here, A=B i.e. A is an improper subset of B.
Note: