Q:

Language of Regular Expression

I'm trying to teach myself Regular expressions for Automata,
I'm struggling to work out what the output of 
$L((1+01)^*)$ would be
Would it be the star closure of $\{1,01\}$ or star closure of $\{1,0,1\}$?
Thanks.

A:

$L(1+01)=\{1,01\}$, so it’s the star closure of $\{1,01\}$, which consists of all strings over the alphabet $\{0,1\}$ in which every $0$ (if there is one) is immediately followed by a $1$.

