Set Builder Notation Examples
Example 1: Use the set-builder notation to represent the given set.
A = {2, 4, 6, 8,10}
Solution:
Provided set A = {2, 4, 6, 8,10} in the set-builder form is represented as:
{x: x is an even natural number less than 12″}.
Example 2: How should x ≤ 3 or x ≥ 4 be written in set-builder notation?
Solution:
In set builder notation, x ≤ 3 or x ≥ 4 may be written as:
{x ∈ R | x ≤ 3 or x ≥ 4}
Example 3: Use interval notation to represent the set that contains all positive real values.
Solution:
The number that is bigger than 0 would serve as the starting point for the set of positive real numbers, albeit we are unsure of the precise value of this number. Positive real numbers also exist in an unlimited number of combinations. As a result, we may express it as the interval (0, ∞).
Example 4: Decode the symbols that are presented:
(i) 5 ∈ ℚ
(ii) -8 ∉ ℕ
Solution:
Set of natural numbers is N, while the set of rational numbers is Q.
(i) 5 ∈ Q denotes that 5 is a member of a group of rational numbers.
(ii) -8 ∉ N indicates that -8 does not fall under the category of natural numbers.
Set-Builder Notation
Set-builder Notation is a type of mathematical notation used to describe sets by naming their components or highlighting the requirements that each member of the set must meet. Sets are written in the form of {y | (properties of y)} OR {y : (properties of y)} in the set-builder notation, where the condition that fully characterizes each member of the collection replaces the attributes of y.
The elements and properties are separated using the character ‘|’ or ‘:’ The entire set is interpreted as “the set of all elements y” such that (properties of y), while the symbols ‘|’ or ‘:’ are read as “such that.”
This article explores the set-builder notation, symbols used in set-builder notation, examples, representation of sets methods, etc.
Table of Content
- What is Set-Builder Notation?
- Symbols Used in Set Builder Notation
- Representation of Sets Methods
- Tabular or Roster Form
- Examples of Roster Method
- Set-Builder Notation
- Why Do We Use Set Builder Form?
- How to use a Set Builder Notation?
- How to Write a Set Builder Notation?
- How to read Set Builder Notation?
- Set Builder Notation for Domain and Range
- Set Builder Notation Examples
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