2015年电大离散数学作业3答案资料小抄(集合论部分)

形成性考核 作业 1 离散数学作业 3 离散数学 集合 论部分 形成性考核 书面 作业 本课程形成性考核 书面 作业共 3 次，内容 主要分别是 集合论部分、 图论部分、数理逻辑部分的综合练习，基本上是按照考试的题型 （除单项选择题外） 安排练习题目 ，目的是通过综合性书面作业，使同学自己检验学习成果，找出掌握的薄弱知识点，重点复习，争取尽快掌握。 本次形考 书面 作业是第 一 次作业，大家要 认真及时地完成 集合 论部分的 综合练习 作业 。 要求： 将此作业用 A4 纸打印出来，手工书写答题， 字迹工整，解答题 要 有解答过程 ，要求 2010年 11 月 7 日前完成并上交任课教师（不收电 子稿）。 并 在 03 任务界面下方点击“保存”和“交卷”按钮 ， 完成并上交任课教师 。 一 、填空题 1设集合 1 , 2 , 3 , 1 , 2 AB，则 P(A)-P(B )= 1,2,2,3,1,3,1,2,3 ， A B= , 2设集合 A 有 10 个元素，那么 A 的幂集合 P(A)的元素个数为 1024 3 设集合 A=0, 1, 2, 3， B=2, 3, 4, 5， R 是 A 到 B 的二元关系， , BAyxByAxyxR 且且 则 R 的有序对集合为 , 4设集合 A=1, 2, 3, 4 ， B=6, 8, 12， A 到 B 的二元关系 R ,2, ByAxxyyx 那么 R 1 , 5 设集合 A= a, b, c, d， A 上的二元关系 R=, , , ，则 R 具有的性质是 反自反性 6设集合 A= a, b, c, d， A 上的二元关系 R=, , , ， 若在 R 中再增加两个 元素 , ， 则 新 得到的关系 就 具有 对称 性 7 如果 R1 和 R2 是 A 上的自反关系，则 R1 R2， R1 R2， R1-R2 中自反关系有 2 个 8 设 A=1, 2上的二元关系 为 R=|xA， yA, x+y =10，则 R 的自反闭包为 , 9设 R 是 集合 A 上 的等价关系 ，且 1 , 2 , 3 是 A 中 的 元素，则 R 中至少包含 , 等元素 10设集合 A=1, 2， B=a, b，那么集合 A 到 B 的双射函数是 ,或 , 二 、判断说明题 （ 判断下列各题，并说明理由 ） 1 若 集合 A = 1， 2， 3上的 二元关系 R=， ， ，则 (1) R 是 自反 的关系 ； (2) R 是对称的关 系 姓 名： 学 号： 得 分： 教师签名： 形成性考核 作业 2 解： (1) 结论不成立 因为 关系 R 要成为自反的，其中缺少元素 (2) 结论不成立 因为 关系 R 中缺少元素 2如果 R1 和 R2 是 A 上的自反关系，判断结论：“ R-11、 R1 R2、 R1R2 是自反的” 是否成立？并说明理由 解： 结论成立 因为 R1 和 R2 是 A 上的自反关系，即 IAR1， IAR2 由逆关系定义和 IAR1，得 IA R1-1； 由 IAR1， IAR2，得 IA R1 R2， IA R1R2 所以， R1-1、 R1 R2、 R1R2 是自反的 3 若偏序集 的哈斯图如图 一 所示， 则集合 A 的最大元为 a，最小元不存在 错误，按照定义，图中不存在最大元和最小元。 4 设集合 A=1, 2, 3, 4， B=2, 4, 6, 8， ，判断 下列关系 f 是否构成函数 f： BA ，并说明理由 (1) f=, , , ； (2)f=, , ； (3) f=, , , (1) 不构成函数，因为它的定义域 Dom(f) A (2) 也不构成函数，因为它的定义域 Dom(f) A (3) 构成函数，首先它的定义域 Dom(f) =1, 2, 3, 4= A，其次对于 A 中的每一个元素 a，在 B 中都有一个唯一的元素 b，使 f 三 、 计算题 1设 4,2,5,2,1,4,1,5,4,3,2,1 CBAE ，求： (1) (AB)C； (2) (AB)- (BA) (3) P(A) P(C)； (4) AB 解： (1) (AB)C=11,3,5=1,3,5 (2) (AB)- (BA)=1,2,4,5-1=2,4,5 (3) P(A) = ,1,4,1,4 P(C)= ,2,4,2,4 P(A) P(C)=1,1,4 (4) AB= (AB)- (BA)= 2,4,5 a b c d 图 一 g e f h 形成性考核 作业 3 2 设 A=1,2,1,2， B=1,2,1,2，试计算 （ 1）（ AB）； （ 2）（ A B）； （ 3） A B 解： （ 1）（ AB） =1,2 （ 2）（ A B） =1,2 (3) AB , 3 设 A=1， 2， 3， 4， 5， R=|xA， yA 且 x+y4， S=|xA， yA 且 x+y0，试求 R， S， RS， SR， R-1， S-1， r(S)， s(R) 解： R=, S= RS= SR= R-1=, S-1= r(S)= , s(R)= , 4 设 A=1, 2, 3, 4, 5, 6, 7, 8， R 是 A 上的整除关系， B=2, 4, 6 (1) 写出关系 R 的表示式； (2 )画出关系 R 的哈斯图； (3) 求出集合 B 的最大元、最小元 解： (1) R=, (2) (3) 集合 B 没有最大元，最小元是 2 四 、 证明 题 1 试证明集 合等 式： A (BC)=(AB) (AC) 证：设，若 x A (BC)，则 x A 或 x BC， 即 x A 或 x B 且 x A 或 x C 即 x AB 且 x AC ， 即 x T=(AB) (AC)， 所以 A (BC) (AB) (AC) 1 2 3 4 6 5 7 8 关系 R 的哈斯图 形成性考核 作业 4 反之，若 x (AB) (AC)，则 x AB 且 x AC， 即 x A 或 x B 且 x A 或 x C， 即 x A 或 x BC， 即 x A (BC)， 所以 (AB) (AC) A (BC) 因此 A (BC)=(AB) (AC) 2试证明集合等 式 A (BC)=(AB) (AC) 证明：设 S=A (B C)， T=(A B) (A C)， 若 x S，则 x A 且 x B C，即 x A 且 x B 或 x A 且 x C， 也即 x A B 或 x A C ，即 x T，所以 ST 反之，若 x T，则 x A B 或 x A C， 即 x A 且 x B 或 x A 且 x C 也即 x A 且 x B C，即 x S， 所以 TS 因此 T=S 3 对任意三个集合 A, B 和 C，试证 明： 若 A B = A C，且 A ，则 B = C 证明 ： 设 xA， yB，则 AB， 因为 AB = AC，故 AC，则有 yC， 所以 B C 设 xA， zC，则 AC， 因为 AB = AC，故 AB，则有 zB，所以 CB 故得 A=B 4 试证明：若 R 与 S 是集合 A 上的自反关系，则 RS 也是集合 A 上的自反关系 R1 和 R2 是自反的 ， x A， R1， R2， 则 R1R2， 所以 R1R2 是自反的 形成性考核 作业 5 请您删除一下内容 ， O( _ )O 谢谢 ！ 2015 年中央电大期末复习考试小抄大全 ， 电大期末考试必备小抄 ， 电大考试必过小抄 After earning his spurs in the kitchens of The Westin, The Sheraton, Sens on the Bund, and a sprinkling of other top-notch venues, Simpson Lu fi nally got the chance to become his own boss in November 2010. Sort of. The Shanghai-born chef might not actually own California Pizza Kitchen (CPK) but he is in sole charge of both kitchen and frontof- house at this Sinan Mansionsstalwart. Its certainly a responsibility to be the head chef, and then to have to manage the rest of the restaurant as well, the 31-year-old tells Enjoy Shanghai. In hotels, for example, these jobs are strictly demarcated, so its a great opportunity to learn how a business operates across the board. It was a task that management back in sunny California evidently felt he was ready for, and a vote of confi dence from a company that, to date, has opened 250 outlets in 11 countries. And for added pressure, the Shanghai branch was also CPKs China debut. For sure it was a big step, and unlike all their other Asia operations that are franchises, they decided to manage it directly to begin with, says Simpson. Two years ago a private franchisee took over the lease, but the links to CPK headquarters are still strong, with a mainland-based brand ambassador on hand to ensure the business adheres to its ethos of creating innovative, hearth-baked pizzas, a slice of PR blurb that Simpson insists lives up to the hype. They are very innovative, he says. The problem with most fast food places is that they use the same sauce on every pizza and just change the toppings. Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the toppings perfectly. The largely local customer base evidently agrees and on Saturday and Sunday, at least, the place is teeming. The kids-eat-for-free policy at weekends is undoubtedly a big draw, as well as is the spacious second-fl oor layout overlooked by a canopy of green from Fuxing Park over the road. The company is also focusing on increasing brand recognition and in recent years has taken part in outside events such as the regular California Week. Still, the sta are honest enough to admit that business could be better； as good, in fact, as in CPKs second outlet in the popular Kerry Parkside shopping mall in Pudong. Sinan Mansions has really struggled to get the number of visitors that were envisaged when it first opened, and it hasnt been easy for any of the tenants here, adds Simpson. Were planning a third outlet in the city in 2015, and we will probably choose a shopping mall again because of the better foot traffic. The tearooms once frequented by Coco Chanel and Marcel Proust are upping sticks and coming to Shanghai, Xu Junqian visits the Parisian outpost with sweet treats. One thing the century-old Parisian tearoom Angelina has shown is that legendary fashion designer Coco Chanel not only had style and glamor but also boasted great taste in food, pastries in particular. One of the most popular tearooms in Paris, Angelina is famous for having once been frequented by celebrities such as Chanel and writer Marcel Proust. Now Angelina has packed up its French ambience, efficient service, and beautiful, comforting desserts and flown them to Shanghai. At the flagship dine-in and take-out space in Shanghai, everything mimics the original tearoom designed from the beginning of the 20th century, in Paris, the height of Belle Epoque. The paintings on the wall, for example, are exactly the same as the one that depicts the landscape of southern France, the hometown of the owner； and the small tables are intentional imitations of the ones that Coco Chanel once sat at every afternoon for hot chocolate. The famous hot chocolate, known as LAfricain, is a luxurious mixture of four types of cocoa beans imported from Africa, blended in Paris and then shipped to Shanghai. Its sinfully sweet, rich and thick as if putting a bar of melting chocolate directly on the tongue and the fresh whipped cream on the side makes a light, but equally gratifying contrast. It is also sold in glass bottles as takeaway. The signature Mont-Blanc chestnut cake consists of three parts: the pureed chestnut on top, the vanilla cream like stuffing, and the meringue as base. Get all three layers in one scoop, not only for the different textures but also various flavors of sweetness. The dessert has maintained its popularity for a century, even in a country like France, perhaps the worlds most competitive place for desserts. A much overlooked pairing, is the Paris-New York choux pastry and N226 chocolate flavored tea. The choux pastry is a mouthful of airy pecan-flavored whipped cream, while the tea, a blend of black teas from China and Ceylon, cocoa and rose petals, offers a more subtle fragrance of flowers and chocolate. Ordering these two items, featuring a muted sweetness, makes it easier for you to fit into your little black dress. Breakfast, brunch, lunch and light supper are also served at the tearoom, a hub of many cultures and takes in a mix of different styles of French cuisines, according to the management team. The semi-cooked foie gras terrine, is seductive and deceptive. Its generously served at the size and shape of a toast, while the actual brioche toast is baked into a curved slice dipped with fig chutney. The flavor, however, is honest: strong, smooth and sublime. And you dont actually need the toast for crunchiness. This is the season for high teas, with dainty cups of fine china and little pastries that appeal to both visual and physical appetites. But there is one high tea with a difference, and Pauline D. Loh finds out just exactly why it is special. Earl Grey tea and macarons are all very well for the crucial recuperative break in-between intensive bouts of holiday season shopping. And for those who prefer savory to sweet, there is still the selection of classic Chinese snacks called dim sum to satisfy and satiate. High tea is a meal to eat with eye and mouth, an in-between indulgence that should be light enough not to spoil dinner, but sufficiently robust to take the edge off the hunger that strikes hours after lunch. The afternoon tea special at Shang-Xi at the Four Seasons Hotel Pudong has just the right elements. It is a pampering meal, with touches of luxury that make the high tea session a treat in itself. Whole baby abalones are braised and then topped on a shortcrust pastry shell, a sort of Chinese version of the Western vol-au-vent, but classier. Even classier is the dim sum staple shrimp dumpling or hargow, upgraded with the addition of slivers of midnight dark truffles. This is a master touch, and chef Simon Choi, who presides unchallenged at Shang-Xi, has scored a winner again. Sweet prawns and aromatic truffles whats not to love? His masterful craftsmanship is exhibited in yet another pastry a sweet pastry that is shaped to look like a walnut, but which you can put straight into the mouth. It crumbles immediately, and the slightly sweet, nutty morsel is so easy to eat youll probably reach straight for another. My favorite is the dessert that goes by the name yangzhi ganlu, or ambrosia from the gods. The hotel calls it chilled mango cream with sago, pomelo and birds nest made with ingredients that resonate with every female soul. It does taste like ambrosia, with the sweet-sour fragrance of the mango forming the first layer of taste and sensation, and the pomelo sacs and sago pearls providing the t