Relational Model Practice Problems
Coverage: [FCBD] Chapter 3
 Which approach to converting an E/R design involving entity sets
which participate in isa relationships to a relational design
requires more relations: the E/R approach or the OO approach?
 Exercise 3.1.2 (p. 65) of [FCDB].
 Exercises for §3.2 (pp. 7576) of [FCDB].
 Exercises for §3.3 (pp. 8082) of [FCDB].
 Exercises for §3.4 (pp. 8889) of [FCDB].
 Does the definition of FD preclude the case in which the lhs
is the empty set (i.e., {} → A)? If not, explain the meaning
of such a dependency?
 Prove that Armstrong's transitivity axiom is sound (i.e.,
every relation which satisfies the FD X → Y
and Y → Z must also satisfy the FD X → Z).
 Using only Armstrong's axioms and the FD's: {AB → C,
A → BE, C → D},
give a complete derivation of the FD A → D.
 Exercises for §3.5 (pp. 100102) of [FCDB].
 (true/false) Does the following relation instance satisfy the
A → B and BC → A FD's?
A B C

1 2 3
2 2 2
1 3 2
4 2 3

Prove or disprove the following inference rules for FD's. A
proof can be made either by a proof argument or by using
Armstrong's axioms. A disproof should be performed
by demonstrating a relation instance which satisfies the conditions
and FD's on the lhs of the inference rule, but does not satisfy the
FD's on the rhs.
 {W → Y, X → Z} =
{WX → Y}
 {X → Y} and Z ⊆ Y
= {X → Z}
 {X → Y, X → W,
WY → Z} = {X → Z}
 {XY → Z, Y → W} =
{XW → Z}
 {X → Z, Y → Z} =
{X → Y}
 {X → Y, XY → Z} =
{X → Z}
 {X → Y, Z → W} =
{XZ → YW}
 {XY → Z, Z → X} =
{Z → Y}
 {X → Y, Y → Z} =
{X → YZ}
 {XY → Z, Z → W} =
{X → W}
 Are the following two sets of FD's F and G equivalent?
F = {A → C, AC → D,
E → AD, E → H}
G = {A → CD, E → AH}
 Consider the following sets of
FD's over the relation R(A, B, C):
 F_{1} = {A → B, B → C}
 F_{2} = {A → B, A → C}
 F_{3} = {A → B, A B → C}
Identify all sets above which follow from a) F_{1}
b) F_{2}, and c) F_{3}.
Which pairs of these sets of
FD's (F_{1} and F_{2}, F_{2} and
F_{3}, and
F_{1} and F_{3}) are equivalent to each other?
 Consider the following set of
FD's over the relation Widgets(source, destination, volume, weight):
source volume > weight
destination > weight
source volume > destination
 Give a minimal set of FD's equivalent to the set above.
 Give one key for the relation Widgets and prove it is a key.
 Any there any other keys? Give reasons.
 Exercises for §3.6 (p. 117) of [FCDB].
 Exercises for §3.7 (pp. 126127) of [FCDB].
