Set Operations
2026-02-21 20:30 Diff
https://brightchamps.com/en-us/math/algebra/set-operations

A set can look different depending on what it contains and how they are grouped. Some sets have no element at all, and some sets have more elements; some may be a part of other sets, and some may have the same elements. Learning the types of sets helps us compare, organize, and solve problems easily in set theory.

Null or Empty or Void Set: A set with no elements is called a null or empty, or void set. The null set can be denoted by ∅ or {}.

Singleton Set: A set consisting of a single element is called a singleton set.

Finite Set: The set that has only a finite number of elements is known as a finite set.

Infinite Set: A set with an infinite number of elements.

Subset: All the elements from set A are found in set B; then A is termed a subset of B. The subset can be denoted as A ⊆ B.

Proper Subset: When A is a subset of B, but A is not equal to B, then A is considered a proper subset of B. A proper subset can be represented as A ⊂ B, where A ≠ B.

Universal Set: The set that consists of all the elements that occur in the discussion is known as a universal set. The universal set can be denoted as U.

Power Set: If A is the given set and all the subsets of A are called the power set of A and are denoted as P(A).

Equal Set: If every element of the set A is also an element of set B, or vice versa, then it is called an equal set. Equal sets are represented as A = B.

Disjoint Sets: If two sets do not have any common elements, it is known as disjoint sets. Disjoint sets are denoted as A ∩ B = ∅. This denotes that the intersection of disjoint sets results in a null set or a set with no elements.