Consider the following schema A=(w, x, y, z) and the...

Consider the following schema $A=(w, x, y, z)$ and the dependencies are $W \rightarrow X, X \rightarrow Y, Y \rightarrow Z$, and $Z \rightarrow W$ Let $A=\left(A_{1}\right.$ and $A_{2}$ ) be a decomposition such that $A_{1} \cap A_{2}=\phi$ The decomposition is (A) In $1 \mathrm{NF}$ and in $2 \mathrm{NF}$ (B) In $2 \mathrm{NF}$ and not in $3 \mathrm{NF}$ (C) In $2 \mathrm{NF}$ and in $3 \mathrm{NF}$ (D) Not in $2 \mathrm{NF}$ and in $3 \mathrm{NF}$

Consider the following schema $A=(w, x, y, z)$ and the dependencies are $W \rightarrow X, X \rightarrow Y, Y \rightarrow Z$, and $Z \rightarrow W$
Let $A=\left(A_{1}\right.$ and $A_{2}$ ) be a decomposition such that $A_{1} \cap A_{2}=\phi$
The decomposition is
(A) In $1 \mathrm{NF}$ and in $2 \mathrm{NF}$
(B) In $2 \mathrm{NF}$ and not in $3 \mathrm{NF}$
(C) In $2 \mathrm{NF}$ and in $3 \mathrm{NF}$
(D) Not in $2 \mathrm{NF}$ and in $3 \mathrm{NF}$

Key Concepts

Functional Dependencies

Functional dependencies express relationships between attributes in a relation, where one set of attributes uniquely determines another set. They are fundamental in understanding the structure of data and form the basis for normalization, which seeks to organize data to reduce redundancy and improve integrity.

Candidate Keys

Candidate keys are minimal sets of attributes that uniquely identify a tuple in a relation. They are critical in normalization because they determine which attributes are prime (part of a candidate key) and non-prime, influencing how the schema is divided to avoid anomalies and maintain data integrity.

Normal Forms

Normal forms are a series of guidelines (such as 1NF, 2NF, 3NF, etc.) used to evaluate the quality of a relational schema. They help in systematically eliminating redundancy and avoiding update, insertion, and deletion anomalies by enforcing rules based on functional dependencies and candidate keys.

Decomposition

Decomposition is the process of breaking a relation into two or more relations that ideally preserve the original data and dependencies. It is a strategy used to achieve higher normal forms by ensuring that each decomposed relation satisfies certain constraints, such as functional dependency preservation and lossless-join property, even if the pieces have no common attributes.

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