Concerning the function:

\[f(x)=\begin{cases} 2 ,\ \ \text{if}\ \space x\in\mathbb{Q}\\-2,\ \ \text{if}\ \space x\notin\mathbb{Q}\ \end{cases},\]

which of the following statement(s) is/are correct?

It is periodic with period 1

It is periodic with period 2

It is non-periodic

It is periodic but fundamental period is not defined.

**Note:** \(\mathbb{Q}\) represents the set of rational numbers.

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