SQL allows duplicate tuples in relations, and correspondingly defines the multiplicity of tuples in the result of joins. Which one of the following queries always gives the same answer as the nested query shown below: select * from R where a in (select S.a from S)

The given query: ```sql select * from R where a in (select S.a from S) ``` checks for membership in the subquery result. Even if S has duplicate values for column a, a tuple in R is output exactly once for each of its occurrences in R, with no multiplication of multiplicity caused by duplicate matching values in S.

Now analyzing the options:

• Option (A):select R.* from R, S where R.a=S.a performs a standard join. If a value of R.a appears $m$ times in S, that tuple from R will be duplicated $m$ times in the output.

• Option (B):select distinct R.* from R,S where R.a=S.a removes duplicate tuples of R, which alters the original multiplicity of identical tuples that were already present in R.

• Option (C):select R.* from R, (select distinct a from S) as S1 where R.a=S1.a eliminates duplicate values from S first. Joining with this deduplicated subquery ensures each tuple of R matches at most once, preserving the exact multiplicity of tuples in R as in the original IN subquery.

• Option (D): Not valid standard SQL syntax.

Thus, (C) is the correct option.