CLASS-6
TYPES OF SETS

TYPES OF SETS -

Sets can be categorized into various types based on their properties and characteristics. Here are some common types of sets:

  1. Finite Set:- A set that contains a specific, countable number of elements. For example, the set of even prime numbers less than 10: {2}.
  2. Infinite Set:- A set that contains an infinite number of elements. The set of natural numbers: {1, 2, 3, ...} is an example of an infinite set.
  3. Empty Set (Null Set):- A set with no elements. It is denoted by the symbol { } or sometimes as ∅.
  4. Singleton Set:- A set containing only one element. For example, the set containing the number 5: {5}.
  5. Equal Set:- Two sets are equal if they contain exactly the same elements, regardless of the order.
  6. Subset:- A set A is a subset of another set B if every element of A is also an element of B. It is denoted as A ⊆ B.
  7. Proper Subset:- A set A is a proper subset of another set B if A is a subset of B but not equal to B. It is denoted as A ⊂ B.
  8. Universal Set:- The set that contains all the elements under consideration in a particular context. It is often denoted by the symbol U.
  9. Power Set:- The power set of a set A is the set of all possible subsets of A, including the empty set and A itself. If A has n elements, its power set will have 2^n elements.
  10. Disjoint Set (Mutually Exclusive Set):- Two sets A and B are disjoint if they have no elements in common; that is, their intersection is the empty set: A ∩ B = ∅.
  11. Complement Set:- The complement of a set A with respect to a universal set U contains all the elements of U that are not in A. It is denoted as A'.
  12. Finite and Infinite Union Sets:- The union of a finite number of sets (finite union) or an infinite number of sets (infinite union). For example, the union of sets {1, 2, 3} and {3, 4, 5} is {1, 2, 3, 4, 5}.
  13. Finite and Infinite Intersection Sets:- The intersection of a finite number of sets (finite intersection) or an infinite number of sets (infinite intersection). For example, the intersection of sets {1, 2, 3} and {3, 4, 5} is {3}.
  14. Commutative Set:- The order of elements does not affect the result of set operations like union and intersection. For example,                                                                 A ∪ B = B ∪ A.
  15. Distributive Set:- Set operations follow distributive laws, similar to arithmetic. For example, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
  16. Interval Set:- A subset of the real numbers that lies between two values. Common types include open intervals, closed intervals, and half-open intervals.

These are just some of the many types of sets found in mathematics and related fields. Different types of sets have distinct properties and applications, making them valuable tools for solving various problems and representing relationships between elements.