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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:**

__Finite Set:-__A set that contains a specific, countable number of elements. For example, the set of even prime numbers less than 10: {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.__Empty Set (Null Set):-__A set with no elements. It is denoted by the symbol { } or sometimes as ∅.__Singleton Set:-__A set containing only one element. For example, the set containing the number 5: {5}.__Equal Set:-__Two sets are equal if they contain exactly the same elements, regardless of the order.__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.__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.__Universal Set:-__The set that contains all the elements under consideration in a particular context. It is often denoted by the symbol U.__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.__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 = ∅.__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'.__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}.__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}.__Commutative Set:-__The order of elements does not affect the result of set operations like union and intersection. For example, A ∪ B = B ∪ A.__Distributive Set:-__Set operations follow distributive laws, similar to arithmetic. For example, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).__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.**