离散数学考试试卷20102011.docVIP

安徽农业大学2010―2011学年第2学期 《 离散数学 》试卷（A卷） 考试形式: 闭卷笔试，2小时 适用专业：　网络工程、计算机、通信工程专业　　　 题 号 一 二 三 四 五 六 总 分 得 分 得分 评阅人 一、选择题：（10小题，每题2分，共20分） 1.Which of the following are statements?（ ）。 (a). Is 2 a positive number? (b). (c). Study logic (d). Shanghai is a large city 2.Which of the following is true proposition?（ ）。 (a). If 2+2=4, then 2+4=8 (b). If 2+3=5, then 3+3=7 (c). IF 2+2=5, then 3+3=6 3.Which of the following relations are functions（ ）。  (a).　  (b). (c). 4.Let I be the set of integers，Which of the following algebraic system are not semigroups for the operator *（ ） ①a*b=lcm（a，b）， ②a*b=a×b ③a*b=a＋b， ④a*b=a-b. 5. Which of the following is one to one?（ ） 6.Use I,Q,R to denote the set of integers, rational and real respectively, which of following are groups? (a). (b). (c). （d） Where = 7.Which of the following is cyclic group? ( )。 (a). (b). (c). 8.Let A={1,2,…,10},which of following are closed on A( )。 (a). (b). (c). (d). 9.Let A={a,b}, which of the following tables define a monoid on A ( )。 * a b * a b * a b a a b a a b a b a b a b b b b b a b (a) (b) (c) 10. Let be a algebraic structure, if there is a element e in A so that for any a∈A then we call e a ( ) (a) semigroup (b) monoid (c) group （d） 二、填空题：（10空，每空2分，共20分） 1. Let A={a，b，c} and ,find r(R),s(R) and t(R). r(R)= s(R)= t(R)= 2. Complete the following table to obtain a semigroup. * a b c a c a b b a b c c a 3.Let（G，*）be a group，if for any a, b in G the identity a*b=b*a holds then（G，*） is called a ( )． 4.Define the function f and g that map R into R by then =（ ），=（ ）。 5. Let（G，*）is a group, if G is a finit