Is the following Grammar LL(1)
Since the entry was already populated, is this a conflict? If yes, what kind? Or since the 2 productions are the same we can just ignore it? Also if the second case is the right one, is the grammar LL(1)?


Although the entry was populated, this is not a conflict since the same rule is put into the table entry $M [ S , ( ]$, which can be ignored. 

However, the grammar is not LL(1). This can be seen from either of the following.


The string ()() has following two different leftmost derivations.
$$S\rightarrow S'\rightarrow (S)SS'\rightarrow (S')SS'\rightarrow ()SS'\rightarrow()S'S'\\
\rightarrow()(S)SS'S'\rightarrow()(S')SS'S'\rightarrow()()SS'S'\\
\rightarrow()()S'S'S'\rightarrow()()S'S'\rightarrow()()S'\rightarrow()()$$
$$S\rightarrow S'\rightarrow (S)SS'\rightarrow (S')SS'\rightarrow ()SS'\rightarrow()S'S'\\
\rightarrow()S'\rightarrow()(S)SS'\rightarrow()(S')SS'\rightarrow()()SS'\\
\rightarrow()()S'S'\rightarrow()()S'\rightarrow()()$$
When we build the table entry $M[S', (]$, it will have two entries, $S' \rightarrow ( S ) S S'$ and $S' \rightarrow\epsilon$.


Although neither the new grammar nor the original grammar is LL(1), the language generated by either of them is LL(1) since it is generated by following LL(1) grammar.

$$S \rightarrow (S)S \mid \epsilon $$