October 23



Cuemath is a teaching platform that offers an online math program to the students so that they can learn the basics of math and solve difficult problems within seconds.

What are sets in mathematics?

A set in mathematics is simply an organized collection of well-defined objects or elements. In other words, a set refers to the collection of elements that are unique. It can have any group of collected items such as type of automobiles, days of a week, letter of alphabets, etc. The representation of a set is done by a capital alphabetic letter.

  • Elements of a set:

Assume a set A = {7,8,9}. In this A is the set and 7, 8, 9 are the elements or members of a set. The elements in a set can’t be repeated but can be in any sequence and are enclosed in a curly bracket. When an element is a part of a set then it is denoted by ‘∈’ and when an element is not part of a set then it is denoted by ‘∉’.

  • The cardinality of a set:
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The cardinal number, order of a set, or cardinality of a set implies a total number of elements in a set. The sets are a collection of unique elements and all elements in a set are related to each other.

How a set can be represented?

  1. Semantic form: This form is used to show what are the elements of a set. For Example, Set B has the first four even natural numbers.
  2. Roster Form: Most common way to represent the set is curly brackets {}. Here elements are separated by commas and their order doesn’t matter. For Example, Set A = {4,5,6,7}.
  3. Set Builder Form: In this form, a vertical bar is used in its representation, with a text that describes the character of elements of a set. For example, B = {k| k is an odd number, k ≤ 10}.
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What are the set formulas?

Following are the most important set formulas:

For any two given sets, say A and B,

  • n(A U B) = n(A) + n(B) – n(A ∩ B)
  • n (A ∩ B) = n(A) + n(B) – n(A U B)
  • n(A) = n(A U B) + n(A ∩ B) – n(B)
  • n(B) = n(A U B) + n(A ∩ B) – n(A)
  • n(A – B) = n(A U B) – n(B)
  • n(A – B) = n(A) – n(A ∩ B)

For any two disjointed sets A and B,

  • n(A U B) = n(A) + n(B)
  • A ∩ B = ∅
  • n(A – B)= n(A)
  • Operations on a set:
  • Union of sets: It is denoted as A ∪ B, a set that contains all elements of two sets set A and set B. For example, Set A = {1,2,3} and Set B = {4,5,6}, then A ∪ B = {1,2,3,4,5,6}.
  • Intersection of sets: It is denoted as A ∩ B, a set that contains all common elements of two sets set A and set B. For example, Set A = {1,2,3} and Set B = {3,4,5}, then A ∩ B = {3}.
  • Complements of sets: The complement of any set, say B, is the set of all elements that are not in set B. It is represented by B’.
  • Cartesian Product of sets: Cartesian product of sets, say set A and set B is a set of all ordered pairs (a,b), where, element of set A is a and, the element of set B is b. For example, set A = {1,2} and set B = {chair, table}, then A × B = {(1×chair),(1×table),(2×chair)(2×table)}.
  • Difference of sets: Set A difference Set B is a set that doesn’t have elements of B but A. For example, A = {1,2,3} and B = {2,3,4}, then A – B = {1}.
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There are different types of sets including several formulas and operations. For a better understanding, we have discussed the basics of the set in this article. Facing difficulty in understanding what set is? Just go to the Cuemath website or read the below-mentioned article.

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