Algebra - Set Theory - Types of sets

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Sets can be divided into various types according to their properties. Let us see types of sets of Algebra here.

1. Finite Set : Finite set is a set whose elements can be counted or of fixed nature. Thus, set containing finite number of elements can be called as a finite set. For example, set A={2,3,4,5}. Here set A is a finite set with four elements.
2. Infinite Set : Infinite set is a set whose elements can not be counted or of not fixed nature. Thus, set containing infinite number of elements called as an infinite set. For example, set N={1,2,3,4,...}. Here set N is an infinite set of natural numbers. Thus, it is not possible to count the number of elements of set N. Here N is an infinite set.
3. Singleton Set : A set which has only one element is called as singleton set. For example, set A={4} is a singular set as the set A contain only one element i.e., 4.
4. Null set : A set which does not have any elements can be called as a null set. A null set is also called as empty or void set. For example, A={x : x ≠ x, x ∈ N} = ∅. As the set A contains no element it may be called as a null set.
5. Subset : If each element of a set say A exists in another set say B, then A can be called as a subset of B. For example, set A={1,2,3} and set B = {1,2,3,4,5}. Here, all elements of set A exist in set B. Thus, set A can be called as a subset of set B. This is denoted by A ⊆ B.
6. Proper subset : Set A is called a proper subset of set B only if all elements of set A exist in set B and set B has at least one element which does not exist in set A. For example, set A={1,2,3} and Set B ={1,2,3,4}. In this case, set A is a proper subset of set B and denoted as A ⊂ B.

Thus, in this chapter, we have seen various types of sets and their denoting methods as part of set theory for NDA & NA exam preparation coaching material.   Previous lesson : How sets are represented ?
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