离散数学形成性考核作业7答案资料小抄(数理逻辑部分).doc

形成性考核作业 姓 名： 学 号： 得 分： 教师签名： 电大离散数学作业7电大离散数学数理逻辑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三次作业，大家要认真及时地完成数理逻辑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12月19日前完成并上交任课教师（不收电子稿）。并在07任务界面下方点击“保存”和“交卷”按钮，以便教师评分。一、填空题1命题公式的真值是 1 2设P：他生病了，Q：他出差了R：我同意他不参加学习. 则命题“如果他生病或出差了，我就同意他不参加学习”符号化的结果为 PQR 3含有三个命题变项P，Q，R的命题公式PÙQ的主析取范式是 (PÙQÙR) (PÙQÙR) 4设P(x)：x是人，Q(x)：x去上课，则命题“有人去上课” 可符号化为 x ( P ( x) Q ( x) 5设个体域Da, b,那么谓词公式消去量词后的等值式为 (A(a) A(b) (B(a) B(b) 6设个体域D1, 2, 3，A(x)为“x大于3”，则谓词公式($x)A(x) 的真值为 0 7谓词命题公式("x)(A(x)ÙB(x) ÚC(y)中的自由变元为 y 8谓词命题公式("x)(P(x) ®Q(x) ÚR(x，y)中的约束变元为 x 三、公式翻译题 1请将语句“今天是天晴”翻译成命题公式解：设P：今天是天晴则该语句符号化为 P 2请将语句“小王去旅游，小李也去旅游”翻译成命题公式 设P：小王去旅游，Q：小李也去旅游则该语句符号化为 PQ 3请将语句“如果明天天下雪，那么我就去滑雪”翻译成命题公式解：设P：明天天下雪 Q：我就去滑雪则该语句符号化为 PQ 4请将语句“他去旅游，仅当他有时间”翻译成命题公式解：设P：他去旅游 Q：他有时间则该语句符号化为 PQ 5请将语句 “有人不去工作”翻译成谓词公式解：设P(x)：x是人 Q(x)：x不去工作则谓词公式为 (x)(P(x)Q(x) 6请将语句“所有人都努力工作”翻译成谓词公式解：设P(x)：x是人 Q(x)：x努力工作则谓词公式为 (x)(P(x) Q(x)四、判断说明题（判断下列各题，并说明理由） 1命题公式ØPÙP的真值是1不正确，PP的真值是0，它是一个永假式，命题公式中的否定律就是PP=F 2命题公式ØPÙ(P®ØQ)ÚP为永真式 正确可以化简P（PQ）P=P（PQ）P=PP=1，所以它是永真式当然方法二是用真值表 3谓词公式是永真式正确xP(x) (yG(x,y) xP(x)=xP(x) (yG(x,y) xP(x)=xP(x) (y(G(x,y) xP(x)=xP(x) (y(G(x,y) xP(x)=xP(x) y(G(x,y) xP(x)=xP(x) xP(x) y(G(x,y)=1y(G(x,y)=1所以该式是永真式 4下面的推理是否正确，请给予说明(1) ("x)A(x)® B(x) 前提引入(2) A(y) ®B(y) US (1)不正确，(1)中(")x的辖域仅是A(x)，而不是A(x) Ù B(x)四计算题1 求P®QÚR的析取范式，合取范式、主析取范式，主合取范式解：PÚ(QR）= PÚQR所以合取范式和析取范式都是PÚQR所以主合取范式就是PÚQR所以主析取范式就是(ØPÙØQ ÙØR) Ú(ØPÙØQÙ R) Ú (ØPÙQÙ ØR) (ØPÙQ ÙR) Ú(PÙØQÙ R) Ú (PÙQÙØ R) Ú (PÙQÙ R)2求命题公式(PÚQ)®(RÚQ) 的主析取范式、主合取范式解：(PÚØQ)®(RÙQ)= Ø(PÚØQ) Ú (RÙQ)= (ØPÙQ) Ú (RÙQ)其中(ØPÙQ)= (ØPÙQ) Ù (RÚØR)= (ØPÙQÙ R) Ú(ØPÙQ ÙØR)其中(RÙQ)= (RÙQ) Ù (PÚØP)= (PÙQÙ R) Ú (ØPÙQ Ù R)所以原式=(ØPÙQÙ R) Ú(ØPÙQ ÙØR) Ú (PÙQÙ R) Ú (ØPÙQ Ù R) =(ØPÙQÙ R) Ú(ØPÙQ ÙØR) Ú (PÙQÙ R) = (ØPÙQ ÙØR) Ú(ØPÙQÙ R) Ú (PÙQÙ R)=m2Úm3Úm7这就是主析取范式所以主合取范式为M0Ù M1Ù M4Ù M5Ù M6可写为(PÚQÚR)Ù (PÚQÚØR) Ù (ØPÚØQÚR) Ù (ØPÚQÚØR) Ù (ØPÚØQÚR)3设谓词公式（1）试写出量词的辖域；（2）指出该公式的自由变元和约束变元解：(1)量词$x的辖域为 P(x,y) ®("z)Q(y,x,z) 量词"z的辖域为Q(y,x,z) 量词"y的辖域为R(y,x)(2) P(x,y)中的x是约束变元，y是自由变元 Q(y,x,z)中的x和z是约束变元，y是自由变元 R(y,x)中的x是自由变元，y是约束变元 4设个体域为D=a1, a2，求谓词公式"y$xP(x,y)消去量词后的等值式；解： "y$xP(x,y)= $xP(x, a1) Ù$xP(x, a2)=( P(a1, a1) Ú P(a2, a1) Ù( P(a1, a2) Ú P(a1, a2)五、证明题 1试证明 (P®(QÚØR)ÙØPÙQ与Ø (PÚØQ)等价 证：(P®(QÚØR)ÙØPÙQÛ(ØPÚ(QÚØR)ÙØPÙQ Û(ØPÚQÚØR)ÙØPÙQ Û(ØPÙØPÙQ)Ú(QÙØPÙQ)Ú(ØRÙØPÙQ) Û(ØPÙQ)Ú(ØPÙQ)Ú(ØPÙQÙØR) ÛØPÙQ （吸收律） ÛØ(PÚØQ) （摩根律）2试证明($x)(P(x) ÙR(x)Þ($x)P(x) Ù ($x)R(x)证明： (1) ($x)(P(x) ÙR(x) P(2) P(a) ÙR(a) ES(1)(3) P(a) T(2)(4) ($x)P(x) EG(3)(5) R(a) T(2)(6) ($x) R(x) EG(5)(7) ($x)(P(x) ÙR(x) T(4)(6)请您删除一下内容，O(_)O谢谢！【China's 10 must-see animations】The Chinese animation industry has seen considerable growth in the last several years. It went through a golden age in the late 1970s and 1980s when successively brilliant animation work was produced. Here are 10 must-see classics from China's animation outpouring that are not to be missed. Let's recall these colorful images that brought the country great joy. Calabash Brothers Calabash Brothers (Chinese: 葫芦娃) is a Chinese animation TV series produced by Shanghai Animation Film Studio. In the 1980s the series was one of the most popular animations in China. It was released at a point when the Chinese animation industry was in a relatively downed state compared to the rest of the international community. Still, the series was translated into 7 different languages. The episodes were produced with a vast amount of paper-cut animations. Black Cat Detective Black Cat Detective (Chinese: 黑猫警长) is a Chinese animation television series produced by the Shanghai Animation Film Studio. It is sometimes known as Mr. Black. The series was originally aired from 1984 to 1987. In June 2006, a rebroadcasting of the original series was announced. Critics bemoan the series' violence, and lack of suitability for children's education. Proponents of the show claim that it is merely for entertainment. Effendi "Effendi", meaning sir and teacher in Turkish, is the respectful name for people who own wisdom and knowledge. The hero's real name was Nasreddin. He was wise and witty and, more importantly, he had the courage to resist the exploitation of noblemen. He was also full of compassion and tried his best to help poor people. Adventure of Shuke and Beita【舒克与贝塔】 Adventure of Shuke and Beita (Chinese: 舒克和贝塔) is a classic animation by Zheng Yuanjie, who is known as King of Fairy Tales in China. Shuke and Beita are two mice who don't want to steal food like other mice. Shuke became a pilot and Beita became a tank driver, and the pair met accidentally and became good friends. Then they befriended a boy named Pipilu. With the help of PiPilu, they co-founded an airline named Shuke Beita Airlines to help other animals. Although there are only 13 episodes in this series, the content is very compact and attractive. The animation shows the preciousness of friendship and how people should be brave when facing difficulties. Even adults recalling this animation today can still feel touched by some scenes. Secrets of the Heavenly Book Secrets of the Heavenly Book, (Chinese: 天书奇谈) also referred to as "Legend of the Sealed Book" or "Tales about the Heavenly Book", was released in 1983. The film was produced with rigorous dubbing and fluid combination of music and vivid animations. The story is based on the classic literature "Ping Yao Zhuan", meaning "The Suppression of the Demons" by Feng Menglong. Yuangong, the deacon, opened the shrine and exposed the holy book to the human world. He carved the book's contents on the stone wall of a white cloud cave in the mountains. He was then punished with guarding the book for life by the jade emperor for breaking heaven's law. In order to pass this holy book to human beings, he would have to get by the antagonist fox. The whole animation is characterized by charming Chinese painting, including pavilions, ancient architecture, rippling streams and crowded markets, which fully demonstrate the unique beauty of China's natural scenery. Pleasant Goat and Big Big Wolf【喜洋洋与灰太狼】 Pleasant Goat and Big Big Wolf (Chinese:喜羊羊与灰太狼) is a Chinese animated television series. The show is about a group of goats living on the Green Pasture, and the story revolves around a clumsy wolf who wants to eat them. It is a popular domestic animation series and has been adapted into movies. Nezha Conquers the Dragon King（Chinese: 哪吒闹海） is an outstanding animation issued by the Ministry of Culture in 1979 and is based on an episode from the Chinese mythological novel "Fengshen Yanyi". A mother gave birth to a ball of flesh shaped like a lotus bud. The father, Li Jing, chopped open the ball, and beautiful boy, Nezha, sprung out. One day, when Nezha was seven years old, he went to the nearby seashore for a swim and killed the third son of the Dragon King who was persecuting local residents. The story primarily revolves around the Dragon King's feud with Nezha over his son's death. Through bravery and wit, Nezha finally broke into the underwater palace and successfully defeated him. The film shows various kinds of attractive sceneries and the traditional culture of China, such as spectacular mountains, elegant sea waves and exquisite ancient Chinese clothes. It has received a variety of awards. Havoc in Heaven The story of Havoc in Heaven（Chinese: 大闹天宫）is based on the earliest chapters of the classic story Journey to the West. The main character is Sun Wukong, aka the Monkey King, who rebels against the Jade Emperor of heaven. The stylized animation and drums and percussion accompaniment used in this film are heavily influenced by Beijing Opera traditions. The name of the movie became a colloquialism in the Chinese language to describe someone making a mess. Regardless that it was an animated film, it still became one of the most influential films in all of Asia. Countless cartoon adaptations that followed have reused the same classic story Journey to the West, yet many consider this 1964 iteration to be the most original, fitting and memorable, The Golden Monkey Defeats a Demon【金猴降妖】 The Golden Monkey Defeats a Demon (Chinese: 金猴降妖), also referred as "The Monkey King Conquers the Demon", is adapted from chapters of the Chinese classics "Journey to the West," or "Monkey" in the Western world. The five-episode animation series tells the story of Monkey King Sun Wukong, who followed Monk Xuan Zang's trip to the West to take the Buddhistic sutra. They met a white bone evil, and the evil transformed human appearances three times to seduce the monk. Twice Monkey King recognized it and brought it down. The monk was unable to recognize the monster and expelled Sun Wukong. Xuan Zang was then captured by the monster. Fortunately Bajie, another apprentice of Xuan Zang, escaped and persuaded the Monkey King to come rescue the monk. Finally, Sun kills the evil and saves Xuan Zang. The outstanding animation has received a variety of awards, including the 6th Hundred Flowers Festival Award and the Chicago International Children's Film Festival Award in 1989. McDull【麦兜】 McDull is a cartoon pig character that was created in Hong Kong by Alice Mak and Brian Tse. Although McDull made his first appearances as a supporting character in the McMug comics, McDull has since become a central character in his own right, attracting a huge following in Hong Kong. The first McDull movie McMug Story My Life as McDull documented his life and the relationship between him and his mother.The McMug Story My Life as McDull is also being translated into French and shown in France. In this version, Mak Bing is the mother of McDull, not his father. 7