2015年電大離散數(shù)學(xué)作業(yè)3答案資料小抄(集合論部分)

形成性考核 作業(yè) 1 離散數(shù)學(xué)作業(yè) 3 離散數(shù)學(xué) 集合 論部分 形成性考核 書面 作業(yè) 本課程形成性考核 書面 作業(yè)共 3 次，內(nèi)容 主要分別是 集合論部分、 圖論部分、數(shù)理邏輯部分的綜合練習(xí)，基本上是按照考試的題型 （除單項(xiàng)選擇題外） 安排練習(xí)題目 ，目的是通過綜合性書面作業(yè)，使同學(xué)自己檢驗(yàn)學(xué)習(xí)成果，找出掌握的薄弱知識點(diǎn)，重點(diǎn)復(fù)習(xí)，爭取盡快掌握。 本次形考 書面 作業(yè)是第 一 次作業(yè)，大家要 認(rèn)真及時地完成 集合 論部分的 綜合練習(xí) 作業(yè) 。 要求： 將此作業(yè)用 A4 紙打印出來，手工書寫答題， 字跡工整，解答題 要 有解答過程 ，要求 2010年 11 月 7 日前完成并上交任課教師（不收電 子稿）。 并 在 03 任務(wù)界面下方點(diǎn)擊“保存”和“交卷”按鈕 ， 完成并上交任課教師 。 一 、填空題 1設(shè)集合 1 , 2 , 3 , 1 , 2 AB，則 P(A)-P(B )= 1,2,2,3,1,3,1,2,3 ， A B= , 2設(shè)集合 A 有 10 個元素，那么 A 的冪集合 P(A)的元素個數(shù)為 1024 3 設(shè)集合 A=0, 1, 2, 3， B=2, 3, 4, 5， R 是 A 到 B 的二元關(guān)系， , BAyxByAxyxR 且且 則 R 的有序?qū)蠟?, 4設(shè)集合 A=1, 2, 3, 4 ， B=6, 8, 12， A 到 B 的二元關(guān)系 R ,2, ByAxxyyx 那么 R 1 , 5 設(shè)集合 A= a, b, c, d， A 上的二元關(guān)系 R=, , , ，則 R 具有的性質(zhì)是 反自反性 6設(shè)集合 A= a, b, c, d， A 上的二元關(guān)系 R=, , , ， 若在 R 中再增加兩個 元素 , ， 則 新 得到的關(guān)系 就 具有 對稱 性 7 如果 R1 和 R2 是 A 上的自反關(guān)系，則 R1 R2， R1 R2， R1-R2 中自反關(guān)系有 2 個 8 設(shè) A=1, 2上的二元關(guān)系 為 R=|xA， yA, x+y =10，則 R 的自反閉包為 , 9設(shè) R 是 集合 A 上 的等價關(guān)系 ，且 1 , 2 , 3 是 A 中 的 元素，則 R 中至少包含 , 等元素 10設(shè)集合 A=1, 2， B=a, b，那么集合 A 到 B 的雙射函數(shù)是 ,或 , 二 、判斷說明題 （ 判斷下列各題，并說明理由 ） 1 若 集合 A = 1， 2， 3上的 二元關(guān)系 R=， ， ，則 (1) R 是 自反 的關(guān)系 ； (2) R 是對稱的關(guān) 系 姓 名： 學(xué) 號： 得 分： 教師簽名： 形成性考核 作業(yè) 2 解： (1) 結(jié)論不成立 因?yàn)?關(guān)系 R 要成為自反的，其中缺少元素 (2) 結(jié)論不成立 因?yàn)?關(guān)系 R 中缺少元素 2如果 R1 和 R2 是 A 上的自反關(guān)系，判斷結(jié)論：“ R-11、 R1 R2、 R1R2 是自反的” 是否成立？并說明理由 解： 結(jié)論成立 因?yàn)?R1 和 R2 是 A 上的自反關(guān)系，即 IAR1， IAR2 由逆關(guān)系定義和 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 的哈斯圖如圖 一 所示， 則集合 A 的最大元為 a，最小元不存在 錯誤，按照定義，圖中不存在最大元和最小元。 4 設(shè)集合 A=1, 2, 3, 4， B=2, 4, 6, 8， ，判斷 下列關(guān)系 f 是否構(gòu)成函數(shù) f： BA ，并說明理由 (1) f=, , , ； (2)f=, , ； (3) f=, , , (1) 不構(gòu)成函數(shù)，因?yàn)樗亩x域 Dom(f) A (2) 也不構(gòu)成函數(shù)，因?yàn)樗亩x域 Dom(f) A (3) 構(gòu)成函數(shù)，首先它的定義域 Dom(f) =1, 2, 3, 4= A，其次對于 A 中的每一個元素 a，在 B 中都有一個唯一的元素 b，使 f 三 、 計(jì)算題 1設(shè) 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 圖 一 g e f h 形成性考核 作業(yè) 3 2 設(shè) A=1,2,1,2， B=1,2,1,2，試計(jì)算 （ 1）（ AB）； （ 2）（ A B）； （ 3） A B 解： （ 1）（ AB） =1,2 （ 2）（ A B） =1,2 (3) AB , 3 設(shè) A=1， 2， 3， 4， 5， R=|xA， yA 且 x+y4， S=|xA， yA 且 x+y0，試求 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 設(shè) A=1, 2, 3, 4, 5, 6, 7, 8， R 是 A 上的整除關(guān)系， B=2, 4, 6 (1) 寫出關(guān)系 R 的表示式； (2 )畫出關(guān)系 R 的哈斯圖； (3) 求出集合 B 的最大元、最小元 解： (1) R=, (2) (3) 集合 B 沒有最大元，最小元是 2 四 、 證明 題 1 試證明集 合等 式： A (BC)=(AB) (AC) 證：設(shè)，若 x A (BC)，則 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 關(guān)系 R 的哈斯圖 形成性考核 作業(yè) 4 反之，若 x (AB) (AC)，則 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試證明集合等 式 A (BC)=(AB) (AC) 證明：設(shè) S=A (B C)， T=(A B) (A C)， 若 x S，則 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，則 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 對任意三個集合 A, B 和 C，試證 明： 若 A B = A C，且 A ，則 B = C 證明 ： 設(shè) xA， yB，則 AB， 因?yàn)?AB = AC，故 AC，則有 yC， 所以 B C 設(shè) xA， zC，則 AC， 因?yàn)?AB = AC，故 AB，則有 zB，所以 CB 故得 A=B 4 試證明：若 R 與 S 是集合 A 上的自反關(guān)系，則 RS 也是集合 A 上的自反關(guān)系 R1 和 R2 是自反的 ， x A， R1， R2， 則 R1R2， 所以 R1R2 是自反的 形成性考核 作業(yè) 5 請您刪除一下內(nèi)容 ， O( _ )O 謝謝 ！ 2015 年中央電大期末復(fù)習(xí)考試小抄大全 ， 電大期末考試必備小抄 ， 電大考試必過小抄 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