Interval and Set Builder Notation

Front

What is set builder notation?

Back

Set builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy. It is typically written in the form { x | property }, meaning 'the set of all x such that the property holds.'

Front

How do you express the solution x ≥ -2 in set builder notation?

Back

{ x | x ≥ -2 }

Front

What is interval notation?

Back

Interval notation is a way of representing a range of numbers using parentheses and brackets. Brackets [ ] indicate that the endpoint is included, while parentheses ( ) indicate that the endpoint is not included.

Front

Express the interval [-8, 8) in set builder notation.

Back

{ x | -8 ≤ x < 8 }

Front

Express the interval (-9, -4] in set builder notation.

Back

{ x | -9 < x ≤ -4 }

Front

What does the notation [3, 5] represent in set builder notation?

Back

{ x | 3 ≤ x ≤ 5 }

Front

How do you express the interval (-7, 15] in set builder notation?

Back

{ x | -7 < x ≤ 15 }

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Front

Convert the inequality x < 4 into interval notation.

Back

(-∞, 4)

Front

Convert the inequality x ≥ 1 into interval notation.

Back

[1, ∞)