Question

Write the given interval in set-builder form: (6, 12]

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,
given interval = (6, 12]
Now given set 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)
hence, set builder form of the given interval can be written as follows: $\{x|x\in\mathbb{R},6<x≤12\}$