Question

Consider a relation with schema R(A, B, C, D) and FD's A -> B, A -> C, C -> D. Which of the following is the {A}+ ?

Select one:
a. {A,B}
b. {A,B,C,D}
c. {A}
d. {A,B,C}

Answer 1

The closure of the set {A}, denoted as {A}+, includes all attributes that can be determined by A. In the given schema with FDs A -> B, A -> C, and C -> D, the closure is {A, B, C, D}.

Step-by-step explanation:

The question is asking for the closure of the set {A} in the context of a relational schema with given functional dependencies (FDs). To find {A}+, the closure of {A}, we look at the FDs and determine all attributes that can be determined by knowing just the value of A.

Starting with A, we can use the FD A -> B to add B to our closure set. This step is based on the definition that if A determines B, then knowing A means we also know B. Next, A -> C allows us to include C. Finally, because C -> D and we have already determined that C is in our closure set, we can also include D. Therefore, by the transitive property of FDs, knowing A allows us to know B, C, and D. The closure set {A}+ is {A, B, C, D}.