Checking if a functional dependency is in a closure

Question

R=(A,B,C,D,E,F,G)

Functional dependencies:
A→B
BF→C
AB→F
D→E

Which of the following FDs are in F+ (the closure of F)? Select all correct answers.

A→F
DF→E
B→E
A→G
ABC→C

We learned about using reflexivity and augmentation to check if they are in F+, but I can't seem to find any in F+, and am wondering if I am doing it wrong

Please read & act on [ask], hits googling 'stackexchange homework' & the downvote arrow mouseover text. Right now you are just asking us to rewrite your textbook & give a bespoke tutorial & do your homework--that is too broad a question. Give the name & edition of your published academic textbook. Show your work following it. Quote definitions, theorems & algorithms you are using. The first place you are stuck explain about why. (Don't just give some milestones. Without your reasoning we can't tell you where you went wrong or right & we have to redo your reasoning instead of just checking it.) — philipxy, Dec 08 '18 at 17:28

score 1 · Accepted Answer · answered Dec 08 '18 at 14:41

How to find if a functional dependency X → Y is contained in the closure F+ of a set of functional dependency F? The simplest way is to compute X+ (the closure of the set of the attribute X with respect to F) and see if Y is contained in such closure.

For instance, to see if A → F is in F+, we compute the closure of A, A+, in the following way:

A+ = A
A+ = AB (since A→B)
A+ = ABF (since AB→F)

and, since F belongs to A+ = {ABF}, we know that A → F is in F+.

This test should be done for all the remaining dependencies.

If I do that, I get A→F ; DF→E ; ABC → C. – Bjorn Eenhoorn Dec 08 '18 at 15:17 — Bjorn Eenhoorn, Dec 08 '18 at 15:17

Checking if a functional dependency is in a closure

1 Answers1

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