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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