1. Sets and its element
A set is a collection of well-defined and well-distinguished objects. The objects that make up a set are called the members or elements of the set.
Usually indicate sets by capital letters like A,B,C or X,Y,Z while the elements in the set by small letters, viz., a, b, c or x, y, z.
Ex: A= {a, b, c, d, e}

2. Methods of describing a set
There are two methods of describing a set.
1. Tabular/roster/enumeration method: Under this method we enumerate or list all the elements of the set within braces.
Ex: A= {2, 3, 4}, A= {a, b, c, d, e}
2. Selector/property builder/rule method: under this method the elements are not listed but are indicated by description of their characteristics.
Ex: A = {x/x is a vowel in English alphabet}

3. Types of sets
Finite set: When the elements of a set can be counted by a finite number of elements then the set is called a finite set.
Ex: A= {1, 2, 3, 4, 5, 6}
Infinite set: If the elements of a set can not be counted in a finite number, the set is called an infinite set.
Ex: A= {1, 2, 3…}
Singleton/Unit set: A set containing only one element is called a singleton or a unit set.
Ex: A= {a}, B={x/x is an integer neither +ve nor -ve}

4. Empty/Null set: Any set which has no element in it is called an empty set. It is denoted by Greek letter (read as phi).
Ex :( i) The set of people who have traveled from earth to the sun is an empty set.
Equal set: two sets A and B are said to be equal if every element of A is also an element of B, and every element of B is also an element of A.
A=B if and only if { x A =x B}
Ex: A= {2, 3}, B= {3, 2, 2, 3} and C={x: x^2-5x+6}
A=B=C

5. If every element of a set B is also an element of a set A then set B is called subset of set A.
B A
And read as “B is a subset of A”
Ex: A={2,3,4,5}, B={2,3,4,5,6,7}
A B
Proper subset: Set A is called proper subset of superset B if each and every element of set A are the set B and at least one element of superset B is not an element of set A.
Ex: A= {1, 2 , 3, 5, 9, 12} B= {1, 2, 2, 3, 5, 9, 12, 12}
C= {1, 2, 2, 3, 3, 5, 9}
C A, A B and A=B