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

Numerical answer

Single correct

• AReflexivity, Augmentation, and Transitivity
• BReflexivity and Augmentation
• CTransitivity
• DAugmentation and Transitivity

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 $X \to Z$

Numerical answer

Single correct

• AA relation with only two attributes is always in BCNF.
• BIf all attributes of a relation are prime attributes, then the relation is in BCNF.
• CEvery relation has at least one non-prime attribute.
• DBCNF decompositions preserve functional dependencies.

Answer key coming soon

Numerical answer

Answer key coming soon

Single correct

• A$D_1$ is a lossless decomposition, but $D_2$ is a lossy decomposition.
• B$D_1$ is a lossy decomposition, but $D_2$ is a lossless decomposition.
• CBoth $D_1$ and $D_2$ are lossless decompositions.
• DBoth $D_1$ and $D_2$ are lossy decompositions.

Answer key coming soon

One or more correct

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

Answer key coming soon

Single correct

• A$R$ has a nontrivial functional dependency $X \to A$, where $X$ is not a superkey and $A$ is a prime attribute.
• B$R$ has a nontrivial functional dependency $X \to A$, where $X$ is not a superkey and $A$ is a non-prime attribute and $X$ is not a proper subset of any key.
• C$R$ has a nontrivial functional dependency $X \to A$, where $X$ is not a superkey and $A$ is a non-prime attribute and $X$ is a proper subset of some key.
• DA cell in $R$ holds a set instead of an atomic value.

Answer key coming soon

Single correct

• ABoth I and II
• BI only
• CII only
• DNeither I nor II

Single correct

• ASchema I
• BSchema II
• CSchema III
• DSchema IV

Single correct

• A$V \to W$, $V \to X$, $Y \to V$, $Y \to Z$
• B$V \to W$, $W \to X$, $Y \to V$, $Y \to Z$
• C$V \to W$, $V \to X$, $Y \to V$, $Y \to X$, $Y \to Z$
• D$V \to W$, $W \to X$, $Y \to V$, $Y \to X$, $Y \to Z$

Answer key coming soon

Single correct

• AVXYZ
• BVWXZ
• CVWXY
• DVWXYZ

Answer key coming soon

Single correct

• A1NF
• B2NF
• C3NF
• DBCNF

Answer key coming soon

Single correct

• A$\{P, R\} \rightarrow \{S, T\}$
• B$\{P, R\} \rightarrow \{R, T\}$
• C$\{P, S\} \rightarrow \{S\}$
• D$\{P, S, U\} \rightarrow \{Q\}$