# Set Builder Notation Mean in Math | Rule For Set Builder Notation

In Mathematics the set builder notation is also used to express **sets** with an interval or an equation. This is used to write and denoted the members of sets, often for sets with an infinite number of members. A set-builder notation describes the members of a set instead of listing the members.

For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the members. The same set could be defined as { x/x is a natural number less than 10 } in set-builder notation.

In this, one or more variable(s) is used that belong to common types of numbers, such as natural numbers, and real numbers integer numbers. In this article learn about using the symbol in set builder notation, the domain, and range, and the uses of set-builder notation, with the help of examples.

**What is set builder Notation?**

Set-builder notation is described as a representation or a notation that can be used to describe a set that is defined by a logical formula that simplifies to be true for every member of the set. It includes one or more than one variables. A set-builder notation defines the members of a set instead of listing the members.

For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the members separated by a comma. It is also said roster form.

The same set could be described as set builder notation

{ x/x is a counting number less than 10 }.

**Rule Method OR SET builder form**

If the members of a set have a common property then they can be defined by describing the property. For example, the members of set A = {0,1,2,3,4,5,6} have a common property, which states that all the members in set A are whole numbers less than 7. No other whole numbers retain this property. Hence, we can write the set X as follows: A = {x : x is a whole number less than 7} which can be read as “ A is the set of elements x such that x is whole numbers less than 7”

The above set can also be written as A = {x : x W, x < 7}.

**For example:**

A = {x | x ∈ W, 6 < x < 12} and is read as “set A is the set of all ‘x’ such that ‘x’ is a whole number between 6 and 12.”

The symbol ∈ (“belongs to”) means “is a member of” and denotes membership of a member in a set.

**Symbol set builder Notation**

The various symbols used to represent set builder notation are as follows:

- The symbol ∈ “is a member of”.
- The symbol ∉ “is not a member of”.
- The symbol N represents all natural numbers
- The symbol W represents the whole number.
- The symbol Z represents integers
- The symbol R represents real numbers
- The symbol Q represents rational numbers
- The symbol
**|**it means such than - The symbol ‘^’ means ‘and’
- The symbol ‘<’ means ‘less than
- the symbol ‘>’ means ‘greater than
- The symbol ‘≤’ means ‘less than and equal’
- The symbol ‘≥’ mans ‘greater than and equal’
- <x< between

## Example with Solution of set builder notation

**Write the given set in set builder notation**

A= {2, 4, 6, 8, 10, 12}

**Solution:** The given set A= {2, 4, 6, 8, 10, 12} in the set-builder form can be written as:

{x: x is an even natural number less than 13}.

Set-builder notation is used to denote infinite numbers of members of a set.

Numbers such as real numbers, integers, and, natural numbers can be easily denoted using the set-builder notation. Also, the set with an interval or equation can be best described by this method.

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