Function Dependency & Decomposition Homework

Due: See class webpage

- (Question 14.26 in text book)
Conside the relation

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

and the following set of functional dependencies on`R`:F = { A, B -> C A -> D, E B -> F F -> G, H D -> I, J }

- What is the key(s) in
`R` - Decompose
`R`losslessly into BCNF

- What is the key(s) in
- (Question 14.27 in text book)
Conside the relation

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

and the following set of functional dependencies on`R`:F = { A, B -> C B, D -> E, F A, D -> G, H A -> I H -> J }

- What are the key(s) in
`R` - Decompose
`R`losslessly into BCNF

- What are the key(s) in
- (Question 14.28 in text book)
Consider the following relation:

Tuple# A B C ---------------------------------------- #1 10 b1 c1 #2 10 b2 c2 #3 11 b4 c1 #4 12 b3 c4 #5 13 b1 c1 #6 14 b3 c4

- Given the above database content, which of the following
functional dependencies
in the above relation ? If the functional dependency cannot hold, explain*may hold***why**by specifying the tuples that**cause**the violation.1. A -> B 2. B -> C 3. C -> B 4. B -> A 5. C -> A

- Does the above relation have a
candidate key ? If it does, what is it ? If it does not, why not ?*potential*

- Given the above database content, which of the following
functional dependencies
- (Adpated from Question 14.29 in text book)
Consider a relation:

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

with the following functional dependencies:A, B -> C C, D -> E D, E -> B

- Compute the closure
`AB`^{+} - Compute the closure
`CD`^{+} - Compute the closure
`DE`^{+}

- Compute the closure
- (Adpated from Question 14.29 in text book)
Consider a relation:

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

with the following functional dependencies:A, B -> C C, D -> E D, E -> B

- Find
**all**the keys in relation`R`

- Find