If a set contains only one element, then it is called a singleton set. A set consisting of a natural number of objects, i.e. In this set, the number of elements is finite. If a given set is not finite, then it will be an infinite set. 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A set is called a finite set if the members of the set can be counted. Natural numbers are a subset of Integers. A set is a collection of distinct objects(elements) which have common property. B = {y: y is the ordinate of a point on a given line}; There are infinite points on a line. It is represented by U. Set T is an infinite set. The set is empty! Depending upon the context, the universal set is decided. From this, we can say that P(A) will have \(2^n\) elements. Singleton set. Empty set is denoted by ϕ. Singleton set. Empty set. So, P = ϕ. Q = {y : y is a whole number which is not a natural number,y ≠ 0}. Infinite set. consider the set, P = {x : x is a leap year between 1904 and 1908}. Set is defined as a well-defined collection of objects. It is not possible to explicitly list out all the elements of an infinite set. Types of Sets Since, a Set is a well – defined collection of objects; depending on the objects and their characteristics, there are many types of Sets which are explained with suitable examples, as follows: – Empty or Null or Void Set Any Set that does not contain any element is called the empty or null or void set. Types of Sets 1. Let now learn the sets types here in this article. If y ≠ 0, then there is no other value possible for y. The different types of sets are as follows: Empty Set. in which number element is finite is said to be a finite set. There is no natural number between 8 and 9. This set is represented by ϕ or {}. If the number of elements in a set is zero or finite, then the set is called a finite set. 1. If a set contains only one element it is called to be a singleton set. Just contrary to the finite set, it will have infinite elements. For Example. These objects are referred to as elements of the set. Finite set. Basically, sets are the collection of distinct elements of the same type. Between 1904 and 1908, there is no leap year. Solution: T = {0, 1, 2, 3, 4, 5, 6, ...} In example 3, we used an ellipsis at the end of the list to indicate that the set goes on forever. If the set is non-empty, it is called a non-empty finite set. Example1. Equivalent sets. All the empty sets also fall into the category of finite sets. Finite Set. ​. B = {y : y is a whole number which is not a natural number}. For convenience, sets are denoted by a capital letter. A set with have infinite number number of elements is called infinite set. A = {x : x is a month in a year}; Set A will have 12 elements, B={y: y is the zero of a polynomial \((x^4~-~6x^2~+~x~+~2)\)}; Set B will have 4 zeroes. A... 2. If a set has only one element, it's known as singleton set. To learn more about sets and other topics, visit our site BYJU’S and find interesting articles on every topic. Two sets are said to be equivalent sets if they have same number of elements. (ii), which has 10 members. Some examples of finite sets are: Examples: 1 + i, 2 - 6i, -5.2i, 4. Here, A and B are equivalent sets because both sets have 4 elements. Integers are a subset of Rational Numbers. An understanding of what subsets are is required before going ahead with Power-set. For e.g. When, these animals are considered collectively, it's called set. Simply, if set P is contained in set Q, P is called subset of superset Q. For example, a basket of apples, a tea set, a set of real numbers, natural numbers, etc. Two sets are said to be disjoint sets if they don't have common element/s. Hence, Q = ϕ. So, B is an infinite set. It is also called Null Set, Vacuous Set or Void Set. Example 1: Write the given statement in three methods of representation of a set: The set of all integers that lies between -1 and 5 Solution: The methods of representations of sets are: Statement Form: { I is the set of integers that lies between -1 and 5} Roster Form: I = { 0,1, 2, 3,4 } Set-builder Form: I = { x: x ∈ I, -1 < x < 5 } Example 2: Find A U B and A ⋂ B and A – B. A grade 5 class is a finite … It may be a finite or infinite set. An empty set is hence defined as: Definition: If a set doesn’t have any elements, it is known as an empty set or null set or void set. Example #2: What is the set of prime number? A set which do not have any element is known as empty set. It is denoted by P(A). Types of Sets. All the other sets are the subsets of the Universal set.

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