Suppose we have a relation $R(X, Y, Z, W)$ with the FD's:
$$X \to Y, Y \to Z, Z \to W$$
Which one of the following decompositions is not lossless (i.e., for some instance of $R$, the natural join of the decomposed relations is not equal to $R$?
- $R_{1}(X, Y), R_{2}(Y, Z), R_{3}(Z, W)$
- $R_{1}(X, Y), R_{2}(X, Z), R_{3}(X, W)$
- $R_{1}(X, W), R_{2}(Y, W), R_{3}(Z, W)$
- None of the above (that is they are all lossless)