Write the following set in the set-builder form: $\{ 2, 4, 8, 16, 32 \}$

(N/A) The given set is $A = \{ 2, 4, 8, 16, 32 \}$.
We observe that each element is a power of $2$:
$2 = 2^{1}$
$4 = 2^{2}$
$8 = 2^{3}$
$16 = 2^{4}$
$32 = 2^{5}$
Thus,the set can be represented in set-builder form as:
$A = \{ x : x = 2^{n}, n \in \mathbb{N} \text{ and } 1 \le n \le 5 \}$