Question from Database Class Consider a schema R A B C D E

Question from Database Class.

Consider a schema R = {A, B, C, D, E} and a set F = {AB®C, C®D, D®BE} of FDs.

Is {A, B, C} a superkey for R? Justify your answer.

Is {A, B, C} a key for R? Justify your answer.

Is R in Boyce-Codd normal form? Justify your answer.

Solution

1. Here A,B,C is a superkey because AB--> C it implies C is a prime. so A and B are super keys

C-->D D is also prime so C is a super key. Therefore A,B and C are super keys.

2. A,B,C is a keyin R. because A is not RHS. so

the key are (BA)⁺ = {A, B}

(CA)⁺ = {A,B,C}

(DA)⁺ = {A, B, C, D}

(EA)⁺ = {A,B,C,D,E}

Therefore, the keys {A,B,C}