Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# Question:Write the following intervals in set-builder form :(i) (-3, 0) (ii) [6 , 12] (iii) (6, 12] (iv) [-23, 5)

Last updated date: 17th Sep 2024
Total views: 90.6k
Views today: 1.90k
Verified
90.6k+ views

Solution:

Hint:

Set-builder notation is a shorthand way to describe a set by indicating the properties that its members must satisfy. In the context of intervals:

• (a, b) represents all numbers between a and b but not including a or b.

• [a, b] includes the endpoints, meaning it represents all numbers between a and b including a and b themselves.

• (a, b] or [a, b) includes only one endpoint.

Step by Step Solution:

(i) (–3, 0)

This interval includes all numbers between -3 and 0, but not -3 and 0 themselves.

In set-builder notation:
$x : -3 < x < 0$

(ii) [6, 12]

This interval includes all numbers between 6 and 12, and also the numbers 6 and 12.

In set-builder notation:

$x : 6 \leq x \leq 12$

(iii) (6, 12]

This interval includes all numbers between 6 and 12, and also the number 12, but not 6.

In set-builder notation:

$x : 6 < x \leq 12$

(iv) [–23, 5]

This interval includes all numbers between -23 and 5, and also the numbers -23 and 5.

In set-builder notation:

$x : -23 \leq x \leq 5$

Note: Set-builder notation is particularly useful when describing sets that cannot be neatly described as intervals or in roster form. For intervals, it provides a clear understanding of the inclusivity or exclusivity of the endpoints.