Description
Question 1: Keys and Superkeys [6 marks]
Consider a relation Q on atomic attributes (A,B,C,D,E) and the following functional dependencies.
BC → A
ABD → CE CD → A
- List all of the superkeys of Q.
- List all of the candidate keys of Q.
- Give one new functional dependency of the form X → Y (with one attribute on each side) such that if your new dependency were added to the list above, the relation Q would have only one candidate key.
Question 2: Closures and Functional Dependencies [4 marks]
Consider a relation R on atomic attributes (A,B,C,D,E,F) and the following functional dependencies.
AB → C
CD → BF AE → C
AD → E
- What is the closure of {A,B,E}?
- The relation R has only one candidate key. What is it?
- What is the highest normal form attained by the relation R under the dependencies above? Choose from 1NF, 2NF, 3NF and BCNF. Justify your answer; answers with no justification will receive no marks.
Question 3: Normal Forms [6 marks]
Consider a relation S on atomic attributes (A,B,C,D,E,F,G,H) and the following functional dependencies.
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ACG → B
B → G C → D G → A
DE → GC
H → EF
DEF → H
- List all of the FDs above that are 3NF violations.
- List all of the FDs above that are BCNF violations. This list will include all of the FDs from part (a), since a 3NF violation is automatically also a BCNF violation.
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