## Description

Q1. (20 points)

Given the following table for a relation:

A B C D E F

Ankara x00 163 1 10 1

İzmir x04 563 2 10 1

İstanbul x08 267 3 20 2

İstanbul x04 543 4 20 3

Bursa x00 896 5 10 5

Erzurum x08 467 6 10 6

Which of the following functional dependencies hold? Justify your answers.

I. B → C

II. AB → C

III. D → BC

IV. AE → F

V. EF → B

Q2. (20 points)

Find candidate key(s) for the following relations based on given functional dependencies.

I. R(A,B,C,D) F = {A → B, BC → AD}

II. R(A,B,C,D,E) F = {E → CB, D → AE, A → CB}

III. R(X,Y,Z,T) F = {T → X, Z → YT, XY → Z}

IV. R(X,Y,Z,T) F = {T → YZ, Y → XZ, XT → Y}

V. R(A,B,C,D,E) F = {AB → CD, D → A, BC → DE, C → DE}

Q3. (20 points)

Given the relation R(X,Y,Z,U,V,T) and F={X → YZV, YZ → UT, T → XY, V → U}

Is this relation in 3NF? If it is not in 3NF, decompose it into smaller relations so that it

satisfies 3NF. In case you decompose it, is the decomposition lossless? Is it dependency

preserving? Justify your answers.

Q4. (20 points)

Given the relation R(A,B,C,D,E) and F={A → CE, C → BD, DE → AB}

Is this relation in BCNF? If it is not in BCNF, decompose it into smaller relations so that it

satisfies BCNF. In case you decompose it, is the decomposition lossless? Is it dependency

preserving? Justify your answers.

Q5. (20 points)

Find the minimal cover for the following set of functional dependencies. Show your work in

each step.

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

F = {A → BC, B → CE, D → E, DE → BC, E → A}

By doing this homework, you agree that you would follow Bilkent University’s policy on plagiarism,

and you accept that all the solutions belong individually to you. You also accept that in case of an act

of plagiarism, you would not get any points from this homework, and disciplinary action will be taken.