Write the following intervals in set-builder form:
(i) (– 3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [–23, 5)
Answers
Step-by-step explanation:
(i) Here, the given interval = (-3, 0)
for finding the set builder form for the given set the values range from - 3 to 0
This means value of any variable x is greater than - 3 and less than 0
Now, set builder form of the given interval can be written as follows:
A = {x:x ϵ R, -3<x<0}
(ii) Here, the given interval = [6, 12]
Now the set of values of any variable for set given will be such that x is greater than 6 (including 6 as the bracket is closed) and less than 12(including 12)
set builder form of the given interval can be written as follows:
A = {x:x ϵR, 6≤x≤12}
(iii) Here, the given interval = (6, 12]
Now the set of values of any variable for set given is such that x is greater than 6 (excluding 6 as the bracket is open) and less than 12 (including 12, as the bracket is closed)
set builder form of the given interval can be written as follows:
A = {x:x ϵR, 6<x≤12}
(iv) Here, the given interval = [-23, 5)
Now the set of values of any variable for given set is such that x is greater than - 23( including 23 as the bracket is closed) and less than 5 (as the bracket is open)
set builder form of the given interval can be written as follows:
A = {x:x ϵR, -23≤x<5}