1 votes 1 votes Consider the relation $R(A,B,C,D,E)$ with $FD\{ A\rightarrow C, D\rightarrow CE\} $. Which of the following decomposition is in 3NF? (A) $R_1(A,C); R_2(B,E); R_3(A,B,D)$ (B) $R_1(A,C); R_2(D,C,E); R_3(A,B,D)$ (C) Already is in 3NF (D) None of these Databases databases database-normalization + – GateAspirant999 asked Nov 12, 2016 GateAspirant999 576 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes $R(A,B,C,D,E)$ with $FD\{ A\rightarrow C, D\rightarrow CE\} $.where ABD is candidate key. is only in 1nf. $R_1(A,C); R_2(D,C,E); R_3(A,B,D)$ is in BCNF but not lossless decompostion , but quetion ask only 3NF no matter lossless or lossy so this is answer Prashant. answered Nov 12, 2016 Prashant. comment Share Follow See all 2 Comments See all 2 2 Comments reply GateAspirant999 commented Nov 12, 2016 reply Follow Share Some doubts: Why option B is lossless decomposition? $R_1 \cap R_3=A$ and $A$ is a superkey in $R_1$. Also $R_2 \cap R_3=D$ and $D$ is a superkey in $R_2$. Also, I guess I have read all decompositions 2NF, 3NF and BCNF are lossless and only BCNF decomposition can be not dependency preserving. Both 2NF and 3NF decompositions are dependency preserving. Why option A is not in 3NF? Is it because it looses dependency $D\rightarrow CE$? 2 votes 2 votes Sona Barman commented Jan 2, 2018 reply Follow Share Is ABD only candidate key? Or other candidate keys are possible? 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Option B will be right option for it Ck::ABD PD=A->D,D->CE So it is by default in 1NF for converting it into 2NF we take closure of the A+ and D+ then we remove transitive dependency if any exist then resulting table will be R1(AC),R2(DCE) and R3(ABD) -->3NF Paras Nath answered Dec 12, 2016 Paras Nath comment Share Follow See 1 comment See all 1 1 comment reply Varun Raj Akula commented Mar 5, 2022 reply Follow Share Option A and B are lossy decomposition. So how can we conclude that these are in 3NF. Can anyone help me on this? 0 votes 0 votes Please log in or register to add a comment.