浙江科技学院考试试卷
…………………………………………………… … … … … … … … … … … … …名线姓订 装 … … … … … … … … … 号…学… … … … … … … … … … … …级…班…业…专… …浙江科技学院
2010 -2011 学年第 2 学期 第三单元测试试卷
考试科目 离散数学 考试方式闭 完成时限 90分钟 拟题人 叶绿 复核人 审核人 2011年6月10日 信息学院 10 年级 计算机科学与技术 专业 学号 班级 姓名 Part I Part II 题序 * 1 2 3 4 5 6 7 8 9 10 11 12 13 总分 得分
Part I (T/F questions, 15 Scores)
In this part, you will have 15 statements. Make your own judgment, and then put T (True) or F (False) after each statement.
1. Let A and B be sets such that any subsets of A?B is a relation from A to B. T )
2. Let R={(1,1),(1,2),,(3,3) ,(3,1) ,(1,3)} be relations on the set A={1,2,3}then R is transitive. ( F ) 3. Let R={(1,1),(2,2),(2,3),(3,3)} be relations on the set A={1,2,3}then R is symmetric. ( F )
4. Let R be a symmetric relation. Then Rn is symmetric for all positive integers n. ( T )
5. Let R and S are reflexive relations on a set A then R?S maybe not reflexive. ( T )
6. Let R={(a,a), (b,b), (c,c), (a,b), (b,c)} be relations on the set A={a,b,c}then R is equivalence relation. ( F ) 7. If R is equivalence relation, then the transitive closure of R is R. ( T ) 8. Let R be relations on a set A, then R maybe symmetric and antisymmetric.
(T )
9. If ? and ? are partition of a given set A, then ?∪? is also a partition of A. (F )
10. Let R and S are equivalence relations on a set A, Let ? be the set of all equivalence class of R, and ? be the set of all equivalence class of S, if R?S, then ?∩? =?. (F )
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浙江科技学院考试试卷
11. Let (S,?) be a Poset such that S is a finite nonempty set, then S has minimal element, and the elements is unique. (F ) 12. Let R and S are relations on a set A, then MR∩S?MR∧MS. ( F ) 13. If a relation R is symmetric .then there is loop at every vertex of its directed graph. (F ) 14. A directed graph of a partial order relation R cannot contain a closed directed path other than loops. ( T ) 15. The Poset(P(S),?), where P(S) is the power set of a set S is not a chain. ( T )
Part II (Chapter 2 Relations and Posets, Chapter 3 Closures of Relations, 85 Scores)
1. (6 points) Let R be the relation {(1, 2), (1, 3), (2, 3), (2, 4), (3, 1)}, and let
3.
S be relation {(2, 1), (3, 1), (3, 2), (4, 2)}. Find S?R, and R 得分
2. (6 points) Determine whether the relations represented by the following
得分 zero-one matrices are partial orders.
?101??100????? a)110 b)010 ???????001???101??
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浙江科技学院考试试卷
得分 3. (6 points) Determine the number of different equivalence relations on a set with three elements by listing them.
得分
4. (6 points)Let R ={ (a , b)∈A| a divides b }, where A={1,2,3,4}. Find the matrix MR of R. Then determine whether R is reflexive, symmetric, or transitive.
得分 5. (6 points) Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric and/or transitive, where (a, b)?R if
and only if a) a is taller than b.
b) a and b were born on the same day. c) a has the same first name as b.
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浙江科技学院考试试卷
6. (6 points) Define a equivalence relations on the set of students in your
得分 discrete mathematics class. Determine the equivalence classes for these equivalence relations.
7. (8 points) Let R be the relation on the set of ordered pairs of positive
得分 integers such that ((a,b),(c,d))?R if and only if ad?bc. Show that R is an equivalence relation.
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