Figure 1: The er diagram for the terrorist database ... - ByteLABS

serial : char(20),
primary key (date, location, serial),
foreign key (date, location)
references Crimes,
foreign key (serial),
references Weapons);
create table Stolen (name : char(30), serial : char(20),
date : char(20), location : char(30),
primary key (name, serial),
foreign key (name)
referencesGroups,
foreign key (serial)
references Weapons);
(c) The query in tuple-relational calculus is:
{P | T ∈ Terrorists ∧ W ∈ Wanted For∧
U ∈ Used In ∧ V ∈ Weapons ∧
T.name = W.name ∧
W.date = U.date ∧ W.location = U.location ∧
U.serial = V.serial ∧
P.name = T.name ∧ P.type = V.type}
2. (a) (i). The cosine between two vectors ⃗x and ⃗y is defined as:
cos(⃗x, ⃗y) =
⃗x · ⃗y
|⃗x||⃗y| =
∑ ni=1
x i y i
√ ∑ni=1
x 2 √ ∑ni=1
y 2 (1)
(ii).
cos(Q, D 1 ) =
0 · 2 + 1 · 4 + 1 · 2 + 0 · 1 + 0 · 0
√
02 + 1 2 + 1 2 + 0 2 + 0 2√ 2 2 + 4 2 + 2 2 + 1 2 + 0 = 6
2 5 √ 2 (2)
cos(Q, D 2 ) =
0 · 0 + 1 · 0 + 1 · 2 + 0 · 2 + 0 · 1
√
02 + 1 2 + 1 2 + 0 2 + 0 2√ 0 2 + 0 2 + 2 2 + 2 2 + 1 = √ 2 (3)
2 2
This means that D 1 is closer to Q than D 2 and will be ranked higher by the
information retrieval engine.
(b) The basic pattern for noun phrases is: DT? JJ* NN. Instead of determiners,
we can have numerals, and instead of simple nouns, we can have compounds
(such as Apogee common stock). This yields the following regular expression:
(DT|CD)? JJ* (NN|JJ)* NN. If we allow pre-nominal determiner phrases such
as each of, we get: (DT IN)? (DT|CD)? JJ* (NN|JJ)* NN.
In CQP notation (as required in the question), this regular expression is:
([pos="DT"] [pos="IN"])? [pos="DT|CD"]? [pos="JJ"]*
[pos="NN|JJ"]* [pos="NN"]
ii