GATE CS Normal Forms questions

Consider the relation scheme $R = (E, F, G, H, I, J, K, L, M, N)$ and the set of functional dependencies $$\left\{ \{E, F \} \to \{G\}, \{F\} \to \{I, J\}, \{E, H\} \to \{K, L\}, \\ \{K\} \to \{M\}, \{L\} \to \{N\}\right\}$$ on $R$. What is the key for $R$?

Consider a join (relation algebra) between relations $r(R)$ and $s(S)$ using the nested loop method. There are $3$ buffers each of size equal to disk block size, out of which one buffer is reserved for intermediate results. Assuming $\text{size}(r(R))<\text{size}(s(S)),$ the join will have fewer number of disk block accesses if

Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation. employee (empId, empName, empAge) dependent (depId, eId, depName, depAge) Consider the following relational algebra query: …

Relation $R$ has eight attributes $\text{ABCDEFGH}$. Fields of $R$ contain only atomic values. $F$= $\text{{CH→G, A→BC, B→CFH, E→A, F→EG}}$ is a set of functional dependencies $(FDs)$ so that $F^+$ is exactly the set of $FDs$ that hold for $R$. How many candidate keys does the relation $R$ have?

Which of the following is TRUE?

Consider a database table T containing two columns $\text{X}$ and $\text{Y}$ each of type $\text{integer}$. After the creation of the table, one record $\text{(X=1, Y=1)}$ is inserted in the table. Let $\text{MX}$ and $\text{MY}$ denote the respective maximum values of $\text{X}$ and $\text{Y}$ among all records in the table at any point in …

Consider a relational table with a single record for each registered student with the following attributes: $\text{Registration\_Num:}$ Unique registration number for each registered student $\text{UID:}$ Unique identity number, unique at the national level for each citizen $\text{BankAccount\_Num:}$ Unique account number at the bank. A student can …

The following functional dependencies hold for relations $R(A, B, C)$ and $S(B, D, E).$ $B \to A$ $A \to C$ The relation $R$ contains $200$ tuples and the relation $S$ contains $100$ tuples. What is the maximum number of tuples possible in the natural join $R \bowtie S$?

Consider the following relational schema: $\text{Suppliers}(\underline{\text{sid:integer}},\text{ sname:string, city:string, street:string})$ $\text{Parts}(\underline{\text{pid:integer}}, \text{ pname:string, color:string})$ $\text{Catalog}(\underline {\text{sid:integer, pid:integer}}, \text{cost:real})$ Assume that, in the suppliers relation above, …

Consider the following relational schemes for a library database: Book (Title, Author, Catalog_no, Publisher, Year, Price) Collection(Title, Author, Catalog_no) with the following functional dependencies: $\text{Title Author }\rightarrow\text{ Catalog\_no}$ $\text{Catalog\_no }\rightarrow\text{ Title Author Publisher Year}$ …

Which one of the following statements is $\text{FALSE}$?

Which one of the following statements about normal forms is $\text{FALSE}?$

Consider the relation Student (name, sex, marks), where the primary key is shown underlined, pertaining to students in a class that has at least one boy and one girl. What does the following relational algebra expression produce? (Note: $\rho$ is the rename operator). …

The relation scheme $\text{Student Performance (name, courseNo, rollNo, grade)}$ has the following functional dependencies: name, courseNo, $\rightarrow$ grade rollNo, courseNo $\rightarrow$ grade name $\rightarrow$ rollNo rollNo $\rightarrow$ name The highest normal form of this relation scheme is

Consider the following functional dependencies in a database. …

From the following instance of a relation schema $R(A,B,C)$, we can conclude that: $$\begin{array}{|l|l|}\hline \textbf{A} & \textbf{B} & \textbf{C} \\ \hline \text{1} & \text{1} & \text{1} \\ \text{1} & \text{1} & \text{0} \\ \text{2} & \text{3} & \text{2} \\ \text{2} & \text{3} & \text{2} \\ \hline \end{array}$$

Relation $R$ is decomposed using a set of functional dependencies, $F$, and relation $S$ is decomposed using another set of functional dependencies, $G$. One decomposition is definitely $\text{BCNF}$, the other is definitely $3NF$, but it is not known which is which. To make a guaranteed identification, which one of the following tests should be …

Relation $R$ with an associated set of functional dependencies, $F$, is decomposed into $\text{BCNF}$. The redundancy (arising out of functional dependencies) in the resulting set of relations is

$R(A,B,C,D)$ is a relation. Which of the following does not have a lossless join, dependency preserving $BCNF$ decomposition?

Given the following relation instance. $$\begin{array}{|l|l|}\hline \text{X} & \text{Y} & \text{Z} \\ \hline \text{1} & \text{4} & \text{2} \\ \text{1} & \text{5} & \text{3} \\ \text{1} & \text{6} & \text{3} \\ \text{3} & \text{2} & \text{2} \\ \hline \end{array}$$ Which of the following functional dependencies are …