Decomposition of a relation R into R1 and R2 is a lossless-join decomposition if at least one of the following functional dependencies are in F+ (Closure of functional dependencies)

R1 ∩ R2 → R1 OR R1 ∩ R2 → R2

**Question 1:**

Let R (A, B, C, D) be a relational schema with the following functional dependencies:

A → B, B → C, C → D and D → B. The decomposition of R into (A, B), (B, C), (B, D)

**(A)** gives a lossless join, and is dependency preserving

**(B)** gives a lossless join, but is not dependency preserving

**(C)** does not give a lossless join, but is dependency preserving

**(D)** does not give a lossless join and is not dependency preserving

Refer this for solution.

**Question 2 **

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

(A) A->B, B->CD

(B) A->B, B->C, C->D

(C) AB->C, C->AD

(D) A ->BCD

Refer this for solution.

Below is the Quiz of previous year GATE Questions

http://quiz.geeksforgeeks.org/dbms/database-design-normal-forms/

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