Set is a collection of well-defined objects which are distinct from each other. Sets are usually denoted by capital letters A, B, C, and elements are usually denoted by small letters a, b,c. If ‘a’ is an element of a set A, then we write an ∈ A and say ‘a’ belongs to A or ‘a’ is in A or ‘a’ is a member of A. If ‘a’ does not belong to A, we write an ∉ A. Standard Notations  N: A set of natural numbers.  W: A set of whole numbers.  Z: A set of integers.  Z + /Z- : A set of all positive/negative integers.  Q: A set of all rational numbers.  Q + /Q- : A set of all positive/ negative rational numbers.  R: A set of real numbers.  R + /R- : A set of all positive/negative real numbers.  C: A set of all complex numbers. Methods for Describing a Set (i) Roster/Listing Method/Tabular Form In this method, a set is described by the listing elements, separated by commas, within braces. e.g., A = {a, e, i, o, u} (ii) Set Builder/Rule Method In this method, we write down a property or rule which gives us all the elements of the set by that rule. e.g.,A = {x : x is a vowel of English alphabets} Types of Sets 1. Finite Set A set containing a finite number of elements or no element. 2. Cardinal Number of a Finite Set The number of elements in a given finite set is called a cardinal number of a finite sets, denoted by n (A). 3. Infinite Set A set containing an infinite number of elements. 4. Empty/Null/Void Set A set containing no element, it is denoted by (φ) or { }. 5. Singleton Set A set containing a single element. 6. Equal Sets Two sets A and B are said to be equal if every element of A is a member of B and every element of B is a member of A.