Is this not the case that lossless-join property is also non-additive join property?
So, when we say that a decomposition follows the "lossless join property" ,it asserts that the "natural join of the decompositions of the relation should not result in spurious tuples(non-additive) or tuples lost(lossy property)".
Since in the above question, it is clearly mentioned that natural join is lossy, doesn't that mean that there are certain tuples lost. i.e s⊂r.
Hence s⊂r poses me as an answer.
Please correct me if I have misinterpreted this.