《离散数学》试题及答案.doc

一、填空题 1 设集合A,B，其中A＝{1,2,3}, B= {1,2}, 则A - B＝____________________; ((A) - ((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_______________________________ __________________________________________________________. 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| |((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＝_____________________________________________________, R2＝______________________________________________________. 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