Normalization & Functional Dependencies

One or more correct

• AIf $(\{P, Q\} \to \{R\}$ and $\{P\} \to \{R\})$, then $\{Q\} \to \{R\}$
• BIf $\{P, Q\} \to \{R\}$, then $(\{P\} \to \{R\}$ or $\{Q\} \to \{R\})$
• CIf $(\{P\} \to \{R\}$ and $\{Q\} \to \{S\})$, then $\{P, Q\} \to \{R, S\}$
• DIf $\{P\} \to \{R\}$, then $\{P, Q\} \to \{R\}$

One or more correct

• AIt is always possible to obtain a dependency-preserving 3NF decomposition of a relation
• BIt is always possible to obtain a dependency-preserving 1NF decomposition of a relation
• CIt is not always possible to obtain a dependency-preserving BCNF decomposition of a relation
• DIt is not always possible to obtain a dependency-preserving 2NF decomposition of a relation

One or more correct

• AThe relation $team$ is NOT in BCNF.
• BThe relations $t1$ and $t2$ are in BCNF.
• CThe decomposition constitutes a lossless join.
• DThe relation $team$ is NOT in 3NF.

One or more correct

• AR1 is in 3NF
• BR2 is in 3NF
• CR1 is NOT in 3NF
• DR2 is NOT in 3NF

One or more correct

• AR can have a multi-attribute key
• BR cannot have a foreign key
• CR cannot have a composite attribute
• DR cannot have more than one candidate key

One or more correct

• A$(X, Y) \to (Z, W)$ implies $X \to (Z, W)$
• B$(X, Y) \to (Z, W)$ implies $(X, Y) \to Z$
• C$\left((X, Y) \to Z \text{ and } W \to Y\right)$ implies $(X, W) \to Z$
• D$(X \to Y \text{ and } Y \to Z)$ implies $X \to Z$

One or more correct

• A$PS \to T$
• B$R \to T$
• C$P \to R$
• D$PS \to Q$

Answer key coming soon