(完整word版)离散数学试卷及答案(17).pdf
离散数学试卷（十七）110 一、判断正误20%（每小题 2 分）1、设 A.B.C 是任意三个集合。（1）若 AB且 BC，则 AC。（）（2）若 AB且 BC，则 AC。（）（3）若 AB且 BC，则 AC。（）（4）A)()()(CABACB。（）（5）(AB)C=(AC)-(BC)。（）2、可能有某种关系，既不是自反的，也不是反自反的。（）、若两图结点数相同，边数相等，度数相同的结点数目相等，则两图是同构的。（）、一个图是平面图，当且仅当它包含与3，3或5在度结点内同构的子图。（）、代数系统中一个元素的左逆元并一定等于该元素的右逆元。（）、群是每个元素都有逆元的半群。（）二、8%将谓词公式),()()()(),()()(zyQzyPyyxQxPx化为前束析取范式与前束合取范式。三、8%设集合 a,b,c,d 上的关系,写出它的关系矩阵和关系图，并用矩阵运算方法求出的传递闭包。四、9%、画一个有一条欧拉回路和一条汉密尔顿回路的图。、画一个有一条欧拉回路，但没有一条汉密尔顿回路的图。、画一个有一条欧拉回路，但有一条汉密尔顿回路的图。离散数学试卷（十七）111 五、10%证明：若图是不连通的，则的补图G是连通的。六、10%证明：循环群的任何子群必定也是循环群。七、12%用规则证明：FAFEDDCBA,。()()()()()(xPxxQxPx)()xQx。八、10%用推理规则证明下式：前提:)()()(),()()()()()(yWyMyyWyMyxSxFx结论：)()(xFxS)(x九、13%若集合（，），（，），（，），|,12212211yxyxyxyxR1、证明 R 是 X 上的等价关系。2、求出 X 关于 R 的商集。一、填空 20%（每小题 2 分）题目1 2 3 4 5 6 文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2离散数学试卷（十七）112（1）（2）（3）（4）（5）答案N N N Y Y Y N N Y N 二、8%),()()()(),()()(zyQzyPyyxQxPx),()()()(),()()(zyQzyPyyxQxPx),()()()(),()()(zyQzyPyyxQxPx 2分),()()()(),()()(zyQzuPuyxQxPx 4分),()(),()()()()(zyQuPyxQxPzux 6分前束析取范式),(),()(),(),()()()()()()(zyQyxQuPyxQzyQxPuPxPzux前束合取范式共 8 分三、8%RM=0000100001010010 1分关系图2 分传递闭包t(R)=1iURi=iiRU41 4分RRRMMM2=00001000010100100000100001010010=0000000010100101RRRMMM23=00000000101001010000100001010010=0000000001011010文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2离散数学试卷（十七）113 RRRMMM34=00000000010110100000100001010010=0000000010100101432RRRRMMMM=0000100011111111 6分t(R)=,共 8 分四、9%五、10%因为 G=不连通，设其连通分支是)2()(,),(1mVGVGm，由于任两个连通分支)(iVG和)()(jiVGj之间不连通，故两结点子集jiVV 与之间所有连线都在G 的补图G中。Vvu,，则有两种情况：（1）u,v，分别属于两个不同结点子集Vi和 Vj，由于 G(Vi),G(Vj)是两连通分支，故(u,v)在不 G 中，故边（u,v）在G中连通。（2）u,v，属于同一个结点子集Vi，可在另一结点子集Vj中任取一点w，故边(u,w)和边(w,v)均在G中，故邻接边(u,w)(w,v)组成的路连接结点u 和 v，即 u,v 在G中也是连通。六、10%文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2离散数学试卷（十七）114 设是循环群,G=(a)，设 是 的子群。且GSeS,，则存在最小正整数m，使得：Sam，对任意Sal，必有0,0,tmrrtml，故：Saaaaaatmltmltmlr)(*即：Saaatmrl)(*所以Sar，任 m 使Sam的最小正整数，且mr0，所以 r=0 即：tmlaa)(这说明 S 中任意元素是ma的乘幂。所以 是以ma为生成元的循环群。七、用 CP 规则证明12%1、(6 分)AP（附加前提）BATI DCBAP DCT I DTI EDTI FEDP FT I FACP 2、因为)()()()()(xxQxPxxxQxxP本题亦即：)()()()()(xxQxPxxQxPx)()(xPxP（附加前提）)()(xPxTE)(ePES)()(xQxPxP)()(eQePUS)(eQT 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ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2离散数学试卷（十七）115)()()(xxQxPxCP 八、10%)()(yWyMyP)()(eWeMES)()(eWeMTE)()(yWyMyEG)()()(yWyMyTE)()()()()()(yWyMyxSxFxP)()(xSxFxT I)()()(xSxFxTE)()(aSaFUS)()(aSaFTE)()(aSaFTE)()()(xSxFxUG九、13%（1）自反性：RyxyxyxyxXyx),(),(,),(故由于(2)对称性：时当RyxyxXyxyx),(),(,),(),(22112211Ryxyxyxyxyxyx),(),(112221121221有亦即（3）传递性：,),(),(),(332211Xyxyxyx时当RyxyxRyxyx),(),(,),(),(33222211Ryxyxyxyxyxyxyxyx),(),(3311133123321221故相加化简得即由等价关系的定义知R 是 X 上的等价关系。2、X/R=R 文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2离散数学试卷（十七）116 文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2文档编码:CQ8J3Y8P1H7 HK3I2C9W10M1 ZN4I4L1P6P2
