Consider the alphabet $\Sigma = \{0, 1\}$, the null/empty string $\lambda$ and the set of strings $X_0, X_1, \text{ and } X_2$ generated by the corresponding non-terminals of a regular grammar. $X_0, X_1, \text{ and } X_2$ are related as follows.
- $X_0 = 1 X_1$
- $X_1 = 0 X_1 + 1 X_2$
- $X_2 = 0 X_1 + \{ \lambda \}$
Which one of the following choices precisely represents the strings in $X_0$?
- $10(0^*+(10)^*)1$
- $10(0^*+(10)^*)^*1$
- $1(0+10)^*1$
- $10(0+10)^*1 +110(0+10)^*1$