一、填空题
1
设集?/p>
A,B
,其?/p>
A
?/p>
{1,2,3}, B= {1,2},
?/p>
A - B
?/p>
________{3}____________;
?/p>
(A) -
?/p>
(B)
?/p>
_____{{3},{1,3},{2,3},{1,2,3}}_______ .
2.
2.
设有限集?/p>
A, |A| = n,
?/p>
|
?/p>
(A×
A)| = __
2
2
n
3.
设集?/p>
A = {
a
,
b
}, B = {1, 2},
则从
A
?/p>
B
的所有映射是
__
?/p>
1
= {(
a
,1), (
b
,1)},
?/p>
2
= {(
a
,2),
(
b
,2)},
?/p>
3
= {(
a
,1), (
b
,2)},
?/p>
4
= {(
a
,2), (
b
,1)};_,
其中双射的是
____
?/p>
3
,
?/p>
4
._
4.
?/p>
?/p>
?/p>
?/p>
?/p>
?/p>
G
?/p>
?/p>
(P
?/p>
Q)
?/p>
R
?/p>
?/p>
G
?/p>
?/p>
?/p>
?/p>
?/p>
?/p>
?/p>
______(P
?/p>
?/p>
Q
?/p>
R)__________________.
5.
?/p>
G
是完全二叉树?/p>
G
?/p>
7
个点,其?/p>
4
个叶点,?/p>
G
的总度数为
___12_______
,分?/p>
点数?/p>
_______3_________.
6
?/p>
A
?/p>
B
为两个集?/p>
, A= {1,2,4}, B = {3,4},
则从
A
?/p>
B
?/p>
_______{4}__________________;
A
?/p>
B
?/p>
_____{1, 2, 3, 4}____________;A
?/p>
B
?/p>
____{1, 2}_________________ .
3.
7
.
?/p>
R
是集?/p>
A
上的等价关系,则
R
所具有的关系的三个特性是
__
自反性;对称性;
传递?/p>
_______________________________.
8
.
设命题公?/p>
G
?/p>
?/p>
(P
?/p>
(Q
?/p>
R))
,则使公?/p>
G
为真的解释有
____(1, 0, 0)________
?/p>
___
_(1, 0, 1)_________,
____(1, 1, 0)______________________.
9.
设集?/p>
A
?/p>
{1,2,3,4}, A
上的关系
R
1
= {(1,4),(2,3),(3,2)}, R
1
= {(2,1),(3,2),(4,3)},
?/p>
R
1
?/p>
R
2
= _{(1,3),(2,2),(3,1)}__________,R
2
?/p>
R
1
=___{(2,4),(3,3),(4,2)}_____
__,
R
1
2
=_____{(2,2),(3,3)}__________________.
4.
10.
设有限集
A, B
?/p>
|A| = m, |B| = n,
?/p>
| |
?/p>
(A
?/p>
B)| = ___2
m
?/p>
n
_____.
11
?/p>
A,B,R
是三个集合,
其中
R
是实数集?/p>
A = {x | -1
?/p>
x
?/p>
1, x
?/p>
R}, B = {x | 0
?/p>
x < 2, x
?/p>
R},
?/p>
A-B = _{x | -1
?/p>
x < 0, x
?/p>
R}_______ , B-A = __{x | 1 < x < 2, x
?/p>
R}_____ ,
A
?/p>
B =
___{x | 0
?/p>
x
?/p>
1, x
?/p>
R}_______________________ , .
5.
13.
设集?/p>
A
?/p>
{2, 3, 4, 5, 6}
?/p>
R
?/p>
A
上的整除?/p>
?/p>
R
以集合形?/p>
(
列举?/p>
)
记为
__{(2, 2),(2,
4),(2, 6),(3, 3),(3, 6),(4, 4),(5, 5),(6, 6)}_____________________________
.
6.
14.
设一阶逻辑公式
G =
?/p>
xP(x)
?/p>
xQ(x)
,则
G
的前束范式是
__
?/p>
x(
?/p>
P(x)
?/p>
Q(x))_.
15.
?/p>
G
是具?/p>
8
个顶点的树,?/p>
G
中增?/p>
__21_______
条边才能?/p>
G
变成完全图?/p>
16.
设谓词的定义域为
{
a
,
b
},
将表达式
?/p>
xR(x)
?/p>
?/p>
xS(x)
中量词消除,写成与之对应的命题公
式是
____(R(a)
?/p>
R(b))
?/p>
(S(a)
?/p>
S(b))_______________________.