《离散数学》试题含答案《离散数学》试题含答案
⼀、填空题
1设集合A,B,其中A={1,2,3}, B= {1,2}, 则A - B=____________________; ρ(A) - ρ(B)=
__________________________ .
2. 设有限集合A, |A| = n, 则|ρ(A×A)| = __________________________.
3.设集合A = {a, b}, B = {1, 2}, 则从A到B的所有映射是__________________________ _____________, 其中双射的是
__________________________.
4. 已知命题公式G=?(P→Q)∧R,则G的主析取范式是_______________________________
__________________________________________________________.
5.设G是完全⼆叉树,G有7个点,其中4个叶点,则G的总度数为__________,分枝点数为________________.
6设A、B为两个集合, A= {1,2,4}, B = {3,4}, 则从A?B=_________________________; A?B=
_________________________;A-B=_____________________ .
7. 设R是集合A上的等价关系,则R所具有的关系的三个特性是______________________,
________________________, _______________________________.
8. 设命题公式G=?(P→(Q∧R)),则使公式G为真的解释有__________________________,
_____________________________, __________________________.
9. 设集合A={1,2,3,4}, A上的关系R1 = {(1,4),(2,3),(3,2)}, R1 = {(2,1),(3,2),(4,3)}, 则R1?R2 =
________________________,R2?R1 =____________________________, R12
=________________________.
10. 设有限集A, B,|A| = m, |B| = n, 则| |ρ(A?B)| = _____________________________.
11设A,B,R是三个集合,其中R是实数集,A = {x | -1≤x≤1, x∈R}, B = {x | 0≤x < 2, x∈R},则A-B =
__________________________ , B-A = __________________________ ,
A∩B = __________________________ , .
13.设集合A={2, 3, 4, 5, 6},R是A上的整除,则R以集合形式(列举法)记为___________
_______________________________________________________.
14. 设⼀阶逻辑公式G = ?xP(x)→?xQ(x),则G的前束范式是__________________________ _____.
15.设G是具有8个顶点的树,则G中增加_________条边才能把G变成完全图。
16. 设谓词的定义域为{a, b},将表达式?xR(x)→?xS(x)中量词消除,写成与之对应的命题公式是
__________________________________________________________________________.
17. 设集合A={1, 2, 3, 4},A上的⼆元关系R={(1,1),(1,2),(2,3)}, S={(1,3),(2,3),(3,2)}。则R?S=
_____________________________________________________, R 2=
______________________________________________________. ⼆、选择题
1 设集合A={2,{a},3,4},B = {{a},3,4,1},E 为全集,则下列命题正确的是( )。 (A){2}∈A (B){a}?A (C)??{{a}}?B ?E (D)
{{a},1,3,4}?B.
2 设集合A={1,2,3},A 上的关系R ={(1,1),(2,2),(2,3),(3,2),(3,3)},则R 不具备( ).
(A)⾃反性 (B)传递性 (C)对称性