《离散数学》试题及答案

一、填空题

1 设集合A,B，其中A＝{1,2,3}, B= {1,2}, 则A - B＝____________________; (B)＝ __________________________ .

2. 设有限集合A, |A| = n, 则 | (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_______________________________ __________________________________________________________.

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)}, R2 = {(2,1),(3,2),(4,3)}, 则

R1 R2 = ________________________,R2 R1 =____________________________, R12 =________________________.

(A) -

10. 设有限集A, B，|A| = m, |B| = n, 则| | (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__________________________ _____.

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＝_____________________________________________________, R2＝______________________________________________________.