# Solved Homework: Question: Consider a relation R with 6 attributes S, U, N, D, A, Y. You are given the following Functional …

Consider a relation R with 6 attributes S, U, N, D, A, Y. You are given the following Functional Dependencies:

SA à Y

UNà A

U à S

SA à U

S à D

R is in 1NF so one student first decomposes the relation R into R1(S,A, Y ) and R2(S, U, N, D, Y), he concludes that:

(a) this decomposition is lossless join

(b) R2(S, U, N, D, Y) is in BCNF

(c) this decomposition is dependency preserving

State whether each of his conclusions is true or false and justify very concisely.

R(S, U, N, D, A, Y)

Dependencies:

SA > Y
UN > A
U > S
SA > U
S > D

(a) this decomposition is lossless join

Decomposing the relation R into R1(S,A, Y ) and R2(S, U, N, D, Y) is lossless join as projecting the data from R1 and R2 will give us back the same results.

(b) R2(S, U, N, D, Y) is in BCNF

R2(S, U, N, D, Y) is not in BCNF. As FD [S,A –> Y,U] violates BCNF as the LHS is not super-key.

(c) this decomposition is dependency preserving

R1 and R2 are not dependency preserving.

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