Final answer:
The question addresses whether natural join (R ⋈ S) is equal to Cartesian product (R × S) between relations R and S. Typically, the answer is no, as they are different operations unless there are no common attributes or the common attributes always match between R and S.
Step-by-step explanation:
The question being asked is whether R ⋈ S = R × S is true for relations R and S, where R[AB] and S[CD]. It is asking whether the join or natural join (⋈) of R and S is the same as the Cartesian product (×) of R and S.
The answer is generally no. The join (R ⋈ S) is an operation that combines tuples from R and S that have the same value for all attributes that appear in the schema of both R and S. In contrast, the Cartesian product (R × S) is the set of all possible combinations of tuples from R and S, regardless of their attribute values.
It's important to note that R ⋈ S would be equal to R × S only if there were no common attributes between R and S or if for every pair of tuples (one from R and one from S) the common attributes always have the same values, which is a specific and not generally applicable situation.