Description
Please include your answers in a separate document with your name, surname, section and
ID included. You may type your answers on the computer, or you may write them on paper to
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single pdf file on Moodle.
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.
CS 281 Homework #3
