[Solved] CSC370 Assignment1-Keys and Superkeys

Question 1: Keys and Superkeys

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

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

Consider a relation S on atomic attributes (A,B,C,D,E,F,G,H) and the following functional dependencies.

1

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