Set Theory

In Maths, a set is defined as the collection of well-known objects called elements. The element belongs to the set and can be written using “∈.” For example, element 1 belongs to set A, written as 1∈A. If it does not belong to set A, it is written as 1∉ A. The cardinality is defined as the number of elements of the set. If a set contains five elements, then the cardinal number or cardinality of the set is 5.

The set can be represented using three different forms. The three standard methods are:
  • Statement Form
  • Roster Form
  • Set Builder Form
  • Statement Form

In statement form representation, a detailed description of the set is given. Some of the examples are shown below.
  • The set of positive even integers more than 5 and less than 10
  • The set of all odd numbers less than or equal to 15

Roster Form

In roster form, the elements in the set are represented inside the pair of brackets { } separated by commas. The examples of roster forms are given below: 
  • A set of natural numbers less than 5.
Roster form: N = {1, 2, 3, 4}
  • The set natural numbers greater than 10 and less than 15
Roster form: N = {11, 12, 13, 14}

Set Builder Form

In the set builder form, the set is defined by the property that every element in the set should satisfy. The following is an example of the set-builder form:
  • {x: x is an even number | x >3}
Here, the first part contains the type of numbers, and the second part includes the condition to be satisfied by the set elements.

Set Operations

There are various set operations. Like arithmetic operations in algebra, there are also different operations in set theory,to. They are:
  • Consider two sets, A and B, then
  • Union of sets (A U B)
  • Intersections of sets (A ∩ B)
  • Set Difference: A - B
  • Complement Set
  • Disjoint set
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