Let's analyze the set \( A = {x \mid x \in \mathbb{N}, x^2 = 4} \).
The expression specifies that \( x \) is an element of the natural numbers (\(\mathbb{N}\)), and that \( x^2 \) must equal 4.
To find the values of \( x \) that satisfy \( x^2 = 4 \), we can take the square root:
\[ x = \sqrt{4} = 2 \quad \text{or} \quad x = -\sqrt{4} = -2 \]
Since we are only considering \( x \) in the natural numbers, we only take the positive solution. Therefore, the only natural number that satisfies \( x^2 = 4 \) is:
\[ x = 2 \]
Thus, the set \( A \) can be written as:
\[ A = {2} \]
If there are specific options provided regarding the nature or elements of set \( A \), feel free to share them for further elaboration on which statement is correct!