Option A is True for ALL Decompositions.
Option B is True only for Lossless Decompositions.
Option C is Never True, unless it equal.
Option D is True for lossy Decompositions.
Definition. Formally, a decomposition $\text{D}=\left\{\text{R}_1, \text{R}_2, \ldots, \text{R}_m\right\}$ of $\text{R}$ has the lossless (non-additive) join property with respect to the set of dependencies $\text{F}$ on $\text{R}$ if, for every relation state $r$ of $\text{R}$ that satisfies $\text{F}$, the following holds, where $\ast$ is the $\textsf{NATURAL JOIN}$ of all the relations in $\text{D}: \ast\left(\pi_{\text{R}_1}(r), \ldots, \pi_{\text{R}_m}(r)\right)=r$.
Let $\text{R}$ be a relation schema and let $\text{F}$ be a set of $\text{FDs}$ over $\text{R}$. A decomposition of $\text{R}$ into two schemas with attribute sets $\text{X}$ and $\text{Y}$ is said to be a lossless-join decomposition with respect to $\mathbf{F}$ if for every instance $r$ of $\text{R}$ that satisfies the dependencies in $\text{F}, \pi_\text{X}(r) \bowtie \pi_\text{Y}(r)=r$.
This definition can easily be extended to cover a decomposition of $\text{R}$ into more than two relations. It is easy to see that $r \subseteq \pi_\text{X}(r) \bowtie \pi_\text{Y}(r)$ always holds. In general,
