## Nisha Mittal is teaching live on Unacademy Plus

12. Consider a schema R(A, B, C, D) and following functional dependencies B-> C C-D Then decomposition of R into R1 (A, B), R2 (B, C) and R3 (B, D) is (1) Dependency preserving and lossless join. (2) Lossless join but not dependency preserving. (3) Dependency preserving but not lossless join (4) Not dependency preserving and not lossless jo R(A,B,C,D) R1 (A, B) | R2 (B, C) | R3 (B, D) C -B B-D

12. Consider a schema R(A, B, C, D) and following functional dependencies B-> C C-D Then decomposition of R into R1 (A, B), R2 (B, C) and R3 (B, D) is (1) Dependency preserving and lossless join. (2) Lossless join but not dependency preserving. (3) Dependency preserving but not lossless join (4) Not dependency preserving and not lossless jo R(A,B,C,D) R1 (A, B) R2 (B, C) R3 (B, D) Note : C-> D is also preserved with following two C-> B and B-> D.

12. Consider a schema R(A, B, C, D) and following functional dependencies. A -> B B-> C C-> D D- B Then decomposition of R into R1 (A, B), R2 (B, C) and R3 (B, D) is (1) Dependency preserving and lossless join. (2) Lossless join but not dependency preserving. (3) Dependency preserving but not lossless join. (4) Not dependency preserving and not lossless join. R1n R2 B which is a primary key of R2 R2 n R3 B which is a primary key of both R2 and R3 R1 n R3 B which is a primary key of R3 R1 U R2 U R3 ( A, B,C,D So, above relation is lossless All the dependencies are preserved after the decomposition. So, above decomposition is also dependency preserving. Correct option is (a)

12. Consider a schema R(A, B, C, D) and following functional dependencies. A > B C D 1)DEPENDENCY PRESERVING AND LOSSLESS JOIN. Rin R2- B which is a primary key of R2 R2 n R3 B which is a primary key of both R2 and R3 R1 n R3 B which is a primary key of R3 R1 U R2 U R3 ( A, B,C,D So, above relation is lossless All the dependencies are preserved after the decomposition. So, above decomposition is also dependency preserving. Correct option is (a)

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