I have the following FSA, and the regular language that I found for it:

![enter image description here](https://i.stack.imgur.com/QUkb6.png)

Is this language correct? It doesn't match the solution in the book, but my teacher says there can be multiple equally correct languages. The book's solution looks like this: $(0\cup1)1^{\*}00^{\*}(11^{\*}00^{\*})^{\*}$. Are these two languages equal?