Sets can be classified into many types. Some of which are finite, infinite, subset, universal, proper, singleton set, etc.

Finite Set: A set which contains a definite number of elements is called a finite set.

Infinite Set: A set which contains infinite number of elements is called an infinite set.

Subset: A set X is a subset of set Y (Written as X⊆Y) if every element of X is an element of set Y.

Proper Subset: The term “proper subset” can be defined as “subset of but not equal to”. A Set X is a proper subset of set Y (Written as X⊂YX⊂Y) if every element of X is an element of set Y and |X|<|Y|.

Universal Set: It is a collection of all elements in a particular context or application. All the sets in that context or application are essentially subsets of this universal set. Universal sets are represented as UU.

Empty Set or Null Set: An empty set contains no elements. It is denoted by ∅. As the number of elements in an empty set is finite, empty set is a finite set. The cardinality of empty set or null set is zero.

Singleton Set or Unit Set: Singleton set or unit set contains only one element. A singleton set is denoted by {s}.

Equal Set: If two sets contain the same elements they are said to be equal.

Equivalent Set: If the cardinalities of two sets are same, they are called equivalent sets.

OVERLAPPING Set: Two sets that have at least one common element are called overlapping sets.

In case of overlapping sets −

• N(A∪B)=n(A)+n(B)−n(A∩B)
• n(A∪B)=n(A−B)+n(B−A)+n(A∩B)
• n(A)=n(A−B)+n(A∩B)
• n(B)=n(B−A)+n(A∩B)

DISJOINT Set: Two sets A and B are called disjoint sets if they do not have even one element in common. THEREFORE, disjoint sets have the following properties −

• n(A∩B)=∅
• n(A∪B)=n(A)+n(B)

Sets can be classified into many types. Some of which are finite, infinite, subset, universal, proper, singleton set, etc.

Finite Set: A set which contains a definite number of elements is called a finite set.

Infinite Set: A set which contains infinite number of elements is called an infinite set.

Subset: A set X is a subset of set Y (Written as X⊆Y) if every element of X is an element of set Y.

Proper Subset: The term “proper subset” can be defined as “subset of but not equal to”. A Set X is a proper subset of set Y (Written as X⊂YX⊂Y) if every element of X is an element of set Y and |X|<|Y|.

Universal Set: It is a collection of all elements in a particular context or application. All the sets in that context or application are essentially subsets of this universal set. Universal sets are represented as UU.

Empty Set or Null Set: An empty set contains no elements. It is denoted by ∅. As the number of elements in an empty set is finite, empty set is a finite set. The cardinality of empty set or null set is zero.

Singleton Set or Unit Set: Singleton set or unit set contains only one element. A singleton set is denoted by {s}.

Equal Set: If two sets contain the same elements they are said to be equal.

Equivalent Set: If the cardinalities of two sets are same, they are called equivalent sets.

Overlapping Set: Two sets that have at least one common element are called overlapping sets.

In case of overlapping sets −

Disjoint Set: Two sets A and B are called disjoint sets if they do not have even one element in common. Therefore, disjoint sets have the following properties −