# Language to regular expression

Having difficulty grasping the concept of how a language and a regular expression are related. For example:

(In all cases, the alphabet is $\{0,1\}$)

The language $L = \{100,10,011\}$ ------> Regular expression.

So far, I have:

$(0+1)$ since you can have either $0$ or $1$ in the first part...but...I'm not sure what would follow after that...I've tried making a DFA for it but I feel like I'm overcomplicating it. Any help would be great since I'm fairly confused. Thanks!

If the language is finite like you have given in the question then regular expression is simple just write all string separated by $+$(union). So $$r = 100 + 10 + 011$$ further you have something common in first two string so $$r= 10(0+\epsilon) + 011$$
For that You need to learn three operators $*$ , $+$ and $.$ properly & understand the language given then It will be easy for you to make a regular expression without making a D.F.A..