For two languages $\text{A, B}$ over the alphabet $\Sigma$, let the perfect shuffle of $\text{A}$ and $\text{B}$ be the language
\begin{Bmatrix}
w=a_1 b_1 a_2 b_2 \cdots a_k b_k \text{where} a_1 a_2 \cdots a_k \in \text{A} and b_1 b_2 \cdots b_k \in B.& \\ \text{and} k \in\mathbb{N}
&
\end{Bmatrix}
Consider the following statements.
- If $\text{A}$ and $\text{B}$ are regular, then perfect shuffle of $\text{A}$ and $\text{B}$ is regular.
- If $\text{A}$ and $\text{B}$ are regular, then perfect shuffle of $\text{A}$ and $\text{B}$ is context-free.
- If $\text{A}$ and $\text{B}$ are decidable, then perfect shuffle of $\text{A}$ and $\text{B}$ is decidable.
Which of above statements is/are true?
- All of $\text{(i), (ii) and (iii)}$.
- Only $\text{(i) and (ii)}$.
- Only $\text{(ii)}$.
- Only $\text{(ii) and (iii)}$.
- None of $\text{(i), (ii), (iii)}$ is true.
