This question is about SQL, in SQL Relations are MULTISET, not SET. So, $R$ or $S$ can have duplicated.
A. If $R$ has duplicates, in that case, due to distinct keyword those duplicates will be eliminated in final result. So, $R$ can not have duplicates. If $S$ is empty $RXS$ becomes empty, so $S$ must be non empty. This is true.
B. Here, assume that S is empty. (No duplicates.) Then R X S will be empty. SO this is false.
C. Same argument as B.
D. Assume that $R$ has duplicates. Then Distinct keyword will remove duplicates. So, result of query $!= R$, so This is false.