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I am currently studying about formal languages and automata. I am trying to solve a problem but there is a notation whose meaning I'm not sure of.

I have a question to find out the relationship between two languages $L_1$ and $L_2$:

$L_1:$

$S \to aSa|bS|e$

$L_2 \to L((ab+ba)^*)$

My question is, does it mean that $L(ab+ba)$ is the set $\{ab, ba\}$?

I mean, $L(ab+ba) = L(ab)\cup L(ba)$

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This link confirms my intuition that $L(R)$ where $R$ is a regular expressions simply means "the language produced by the regular expression $R$".

In that case, $ab \in L_2$ but $ab \notin L_1$

In case link is down:

Operators used in regular expressions include:

Union: If R1 and R2 are regular expressions, then R1 | R2 (also written as R1 U R2 or R1 + R2) is also a regular expression. L(R1|R2) = L(R1) U L(R2).

Concatenation: If R1 and R2 are regular expressions, then R1R2 (also written as R1.R2) is also a regular expression. L(R1R2) = L(R1) concatenated with L(R2).

Kleene closure: If R1 is a regular expression, then R1* (the Kleene closure of R1) is also a regular expression. L(R1*) = epsilon U L(R1) U L(R1R1) U L(R1R1R1) U ...

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