How To Interpret Set-Builder Notation

Are you finding it hard to interpret the set-builder notations of a given set in your mathematics exam?

In this lesson,

You will learn the set-builder notations and their meaning with how to interpret a set-builder notation in mathematics.

ALSO SEE: How To Solve Sets With Venn Diagram

Set builder notations and their meaning

  • > means ‘greater than’
  • ≥ means ‘greater than or equal to’
  • < means ‘less than’
  • ≤ means ‘less than or equal to’
  • : means ‘such that’

Interpreting set-builder notations

Let’s take an example.


List the elements in the set

A = {x : -2 ≤ x < 4}.

The set-builder notation above is interpreted as A is a set of elements (x) such that the elements (x) is less than or equal to -2 and less than 4.

In other words,

The list of elements in set (A) will be from -2 to the number closest to 4 (but not 4).


Set A = {x : -2 ≤ x < 4}

= {-2, -1, 0, 1, 2, 3}.

Test yourself

Click on the link below to practice real past questions on Sets from different Mathematics exam.


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