Question

Write the given interval in set-builder form: (-3, 0)

Answer 1

first of all, you should understand how to write in set - builder form ?
this can be understand easily with help of a beautiful example.
Let's consider a set A = {1, 2, 3, 4.. 8}
we have to write in set - builder form.
so, we should write A = $\{x|x<9\:\text{and}\:x\in\mathbb{N}\}$
where The braces { } means " the set of "
" x| " means " all numbers x such that "
everything after the " | " describes that set.
so, in this case it means $\textbf{x is less than 9 and is a natural number}$


now come to the question,
we have to write interval (-3, 0) in set builder form.
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: = {x| x $\in$ R, -3 < x < 0}