Question

Given R (A,B,C,D) and FD's = { A→B, B→C, C→D, D→A}.

What is a right statement?
Select one:
a. {A}+={ACD}
b. {A}+ ={AB}
c. none of others
d. {A}+= {CD}

Answer 1

The closure of {A}, considering the given functional dependencies, is {ABCD}. Thus, the correct answer is 'none of others', as the closure includes all the attributes and not a subset as listed in the options.

Step-by-step explanation:

The question relates to database normalization and the computation of attribute closure for a relation R with attributes A, B, C, and D and a set of functional dependencies (FDs). To find the closure of a set of attributes, we apply the given functional dependencies recursively until no new attributes can be added. Given the FDs A→B, B→C, C→D, and D→A, let's compute the closure of {A}.

• Starting with A, we apply A→B to get {AB}.
• Next, using B→C, we add C to our set to get {ABC}.
• Then, applying C→D, we add D to get {ABCD}.

Since {ABCD} includes all the attributes of R, we can conclude that the closure of {A}, denoted as {A}+, is {ABCD}.

Therefore, the correct answer to the given question would be: {A}+ ={ABCD}, which is not explicitly listed among the options provided. Hence, the response would be 'c. none of others'.