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.