What is Set? Describe different types of sets

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What is Set? Describe different types of sets.
OR
Define the following with suitable examples:
  • Finite set
  • Infinite set
  • Universal set
  • Power set
  • Proper subset
  • Cardinal Number
Solution.
Set: 
A set is a collection of definite well defined objects. 
A set is a collection of objects which are distinct from each other.
Construction of Set:
In construction of set, two methods are commonly used:
1. Roster Method (Enumeration): In this method we prepare a list of objects forming the set, writing the elements one after another between a pair of curly brackets.
For example:
A = {a, b, c, d}.
2. Description Method: In this method we describe the set in symbolic language.
For example:
A set of integer numbers which is divisible by 3 is written as,
A = {x : x is an integer divisible by 3}
Types of Set:
1. Finite set : If a set consisting finite number of elements is known as finite set.
For example:
A = {2, 4, 6, 8}.
2. Infinite set : If a set consisting infinite number of elements is known as infinite set.
For example-
The set of all natural numbers.
A = {1, 2, 3,……}
3. Universal set : A Universal Set is the set of all elements under consideration, denoted by capital U. All other sets are subsets of the universal set.
4. Power set : The set of all subset of a set A, is known as power set of A.
For example:
A = {a, b, c}
Than 
Power set,P(A) = {{∅ }, {a}, {b}, {c}, {d}, {ab}, {ac}, {ad}, {bc}, {bd}, {cd}, {abc}}
5. Proper subset : If B is the subset of A, and B≠A, then B is proper subset of A.
For example:
A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {2, 4, 6, 8}
Than, B ⊂ A. (read as B is the proper subset of A)
6. Singleton set: If a set consisting only 1 element is known as singleton set.
For example:
A = {a}.
7. Equal sets: Two sets A and B consisting of the same elements is known as equal set.
For example:
A = {a, b, c, d} and
B = {a, b, c, d}
8. Empty set: If a set consisting no elements is known as empty set or null set or void set.
For example: 
A = { ∅ }
9. Subset: Suppose A is a given set, and any set B exist exist whose elements are also an element of A,than B is called subset of A.
For example:
A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {2, 4, 6, 8}
Than, B ⊆ A. (read as B is the subset of A)
Cardinal number:
The number of elements in a set is known as cardinal number. Cardinal number is represented by n(A). Where A is set name.
For example: A = {1,2,3} then,
n(A) = 3.