离散数学英文试题A
-
《
离散数学》课程试题
【
A
】卷
201
4
～
2
020
学
年
第
2
学
期
考试时间
120
分钟
期末
考试
本科
考核方式
闭卷笔试
学生类别
计信院软件工程
人数
120
2014
级
十
适用专业或科类
题号
得分
签名
一
年级
七
二
三
四
五
六
八
九
合计
<
/p>
阅卷须知：阅卷用红色墨水笔书写，得分用阿拉伯数字写在每小题题号前，用正分表示，不
得分则在题号前写
0
；大题得
分登录在
对应的分数框内；统一命题的课程应集体阅卷，流水作业；阅卷后要进行复核，发现漏评、漏记或总分统计错
误应及时更正；对评定分数或统分记录进行修改时，修改人必须签名。
特别提醒：学生必须遵守课
程考核纪律，违规者将受到严肃处理。
PLEASE
ANSWER IN CHINESE OR IN ENGLISH!!
1.
Fill the best answer in the blanks (3 points
each
，
15 points in all)
(1) If
A
,
B
, and
C
be sets, then
(
A
–
C
)
–
(
B
–
C
) ___________
A
–
B
.
(2) A relation on a set
A
that is reflexive,
symmetric, and transitive is called
an (or a) ___________relation.
(3)
K
n
has
___________edges.
(4) There are _______
__non-isomorphic rooted trees with four
vertices.
(5)
Assume
that
P
(
x
,
y
)
means
“
x
+
2
y
=
xy
”,
where
x
and
y
are
integers.
Then
the
truth
value
of
the
statement
∀
x
∃
y
P
(
x
,
y
) is _______
__.
2.
Choose the corresponding letter of the best answer
that best completes the statements or
answers the questions among A, B, C,
and D and fill the blanks (3 points
each
，
15 points
in
all).
(1) Suppose
A
= {1, 2, 3}. The following
statement (
) is not true.
A
．
(
A
)
A
B
．
{
}
D
．
{{2}}
(
A
)
(
A
)
C
．
{2,
3}
A
(2) Suppose that
R
and
S
are transitive relations
on a set
A
. Then (
) is transitive.
A
．
R
S
B
．
R
S
C
．
R
S
D
．
R
S
(3)
There are (
) strongly connected components of the
following graph
G
.
A. 1
B. 2
C.
3
D. 4
(4) There are (
)
nonisomorphic undirected trees with 5
vertices.
A. 6
B. 5.
C. 4
D. 3
(5) Suppose
P
(
x
,
y
) is a predicate and the
universe for the variables
x
and
y
is {1,2,3}. Suppose
P
(1,3),
P
(2,1),
P
(2,2),
P
(2,3),
P
(3,1),
P
(3,2) are true, and
P
(
x
,
y
) is false otherwise. The
following statement (
) is true.
A.
∀
y
∃
x
(
P
(
x
,
y
)
→
P
(
y
,
x
))
B.
¬
∃
x
∃
y
(
P
(
x
,
y
)
∧
¬
P
(
y
,
x
))
C.
∀
x
∀
y
(
x
y
→
(
P
(
x
,
y
)
∨
P
(
y
,
x
))
D.
∀
y
∃
x
(
x
≤
y
∧
P
(
x
,
y
))
3. Write
“
”
for true, and
“
”
for false in
the blanks at end of each statement
(3
points
each
，
15
points in all).