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数据库系统基础教程第五章答案_(2).doc
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数据库系统基础教程第五章答案_(2).doc
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Exercise 5.1.1
As a set:
speed
2.66
2.10
1.42
2.80
3.20
2.20
2.00
1.86
3.06
Average = 2.37
As a bag:
speed
2.66
2.10
1.42
2.80
3.20
3.20
2.20
2.20
2.00
2.80
1.86
2.80
3.06
Average = 2.48
Exercise 5.1.2
2 / 19
As a set:
hd
250
80
320
200
300
160
Average = 218
As a bag:
hd
250
250
80
250
250
320
200
250
250
300
160
160
80
Average = 215
Exercise 5.1.3a
As a set:
bore
15
3 / 19
16
14
18
As a bag:
bore
15
16
14
16
15
15
14
18
Exercise 5.1.3b
π
bore
(Ships Classes)
Exercise 5.1.4a
For bags:
On the left-hand side:
Given bags R and S where a tuple
t
appears
n
and
m
times respectively,
the union of bags R and S will have tuple
t
appear
n
+
m
times. The
further union of bag T with the tuple
t
appearing
o
times will have
tuple
t
appear
n
+
m
+
o
times in the final result.
On the right-hand side:
Given bags S and T where a tuple
t
appears
m
and
o
times respectively,
the union of bags R and S will have tuple
t
appear
m
+
o
times. The
further union of bag R with the tuple
t
appearing
n
times will have
tuple
t
appear
m
+
o
+
n
times in the final result.
For sets:
This is a similar case when dealing with bags except the tuple
t
can only
appear at most once in each set. The tuple
t
only appears in the result if all
4 / 19
the sets have the tuple
t
. Otherwise, the tuple
t
will not appear in the
result. Since we cannot have duplicates, the result only has at most one copy
of the tuple
t
.
Exercise 5.1.4b
For bags:
On the left-hand side:
Given bags R and S where a tuple
t
appears
n
and
m
times respectively,
the intersection of bags R and S will have tuple
t
appear min(
n
,
m
)
times. The further intersection of bag T with the tuple
t
appearing
o
times will produce tuple
t
min(
o
, min(
n
,
m
) ) times in the final
result.
On the right-hand side:
Given bags S and T where a tuple
t
appears
m
and
o
times respectively,
the intersection of bags R and S will have tuple
t
appear min(
m
,
o
)
times. The further intersection of bag R with the tuple
t
appearing
n
times will produce tuple
t
min(
n
, min(
m
,
o
) ) times in the final
result.
The intersection of bags R,S and T will yield a result where tuple
t
appears
min(
n,m,o
) times.
For sets:
This is a similar case when dealing with bags except the tuple
t
can only
appear at most once in each set. The tuple
t
only appears in the result if all
the sets have the tuple
t
. Otherwise, the tuple
t
will not appear in the
result.
Exercise 5.1.4c
For bags:
On the left-hand side:
Given that tuple
r
in R, which appears
m
times, can successfully join
with tuple
s
in S, which appears
n
times, we expect the result to
contain
mn
copies. Also given that tuple
t
in T, which appears
o
times,
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