If $(\{P, Q\} \rightarrow\{R\}$ and $\{P\} \rightarrow\{R\})$, then $\{Q\} \rightarrow\{R\}$

If $\{P, Q\} \rightarrow\{R\}$, then $(\{P\} \rightarrow\{R\}$ or $\{Q\} \rightarrow\{R\})$

If $(\{P\} \rightarrow\{R\}$ and $\{Q\} \rightarrow\{S\})$, then $\{P, Q\} \rightarrow\{R, S\}$

If $\{P\} \rightarrow\{R\}$, then $\{P, Q\} \rightarrow\{R\}$

It is always possible to obtain a dependency-preserving 3NF decomposition of a relation

It is always possible to obtain a dependency-preserving 1NF decomposition of a relation

It is not always possible to obtain a dependency-preserving BCNF decomposition of a relation

It is not always possible to obtain a dependency-preserving 2NF decomposition of a relation

$\Pi_P\left(R \bowtie_{R . P=S . X} S\right)$

$\Pi_P\left(S \bowtie_{S . X=R . Q} R\right)$

$\Pi_P\left(R \bowtie_{R . P=S . Y} S\right)$

$\Pi_P\left(S \bowtie_{S . Y=R . Q} R\right)$