【正文】 A∪ ACU ＝ U （ 2） A∩ B? A， A∩ B? B， A? A∪ B， B? A∪ B，（ 3） UC （ A∩ B）＝（ UC A）∪（ UC B） ， UC （ A∪ B）＝（ UC A）∩ （ UC B）（ 4） A∩ B＝ A? A? B， A∪ B＝ A? B? A 第二講映射與函數概念、函數的定義域和圖象 一、映射、函數的有關概念： 映射的定義：設 A， B是兩個集合，如果按照某種對應關系 f,對集合 A中的任何一個元素，在集合 B中都有唯一的元素和它對應，那么，這樣的對應叫做集合 A到集合 B的映射，記作 ： f： A→ B， 像與原像：如果給定一個集合 A到集合 B的映射，那么，和集合 A中的 a對應的集合 B中的 b叫做 a的像， a叫做 b的原像。 A∪ 248。 重要性質：（ 1） A∪ A＝ A， A∩ A＝ A， A∩ 248。 含 n 個元素的集合 A的子集有 2n 個，非空子集有 2n － 1個，非空真子集有 2n － 2個。如果 A? B且 B中至少有一個元素不在 A中，則 A叫 B的真子集，記作 A?B。規(guī)定空集是任何集合的子集 ，即 ? ? A， ??? 。m obil e phones as wel as hel p wi th m edi cal operati ons. I have even been put i nto space rockets and sent to expl ore the Moon and Mars . A nyhow, m y goal i s to provi de hum ans wi th a l i fe of hi gh quali ty. I am now truly fi l ed wi th happi ness that I am a devoted fri end and hel per of the hum an race ! AN DY—TH E AN DRO ID I’m part of an an android football team . About once a year we are alowed to get together to play a game of football. I’m as big as a human . In fact ,I look like one the footballteam I’m a striker so I have to be abl e to run very fast .My puter chi ps hel p m e to mova and thi nk li ke a hum an . For exampl e , I have l earned to si gnal to my teamm ates i n puter l anguages to give m e the bal when I am open and have a good shot for a goal. My fi rat footbal l peti tion was i n N agoya , Japan several years ago .Last year our team went to Seattl e ,Washi ngton in the USA. We won tsecong pl ace . Personal ly , I thi nk the team that won fi rsy pl ace cheated . They had devel oped a new type of program just before the peti ti on. So we need to encourage our programer to i mprove our i ntel i gence are determ i ned to create an even better system . In a way our programm et i s li ke our coach. She program s us wi th m oves to use i f a new si tati on ari ses. In thi s way I can m ake up new moves using my “artifical intelligence “. I would realy like to play against a human team,for I have been programmed to act j ust like them. After all,with the help of my electronic brain which never fets anything ,using my intelligence is what I’m al about! TH E SPO RTIN G RO BO T My nam e i s H ua Fei and I am a sporti ng robot of the 23rd century. I am an expert at high fl yi ng exercises. I jum p from spaceshi p and as I fal l I turn, di ve, ci rcl e and dance until I softl y l and as cl ose as I can to the fini shi ng li ne. Robot petiti ons i n the 23rd century are truly a popul ar sport. Fans from al l over Chi na watch thei r handhel d TVs when a peti ti on es on. Last tim e I look part i n the 78th Ol ym pi c on a fl yi ng i sl and above Brussel s i n the sky. I won the siver m edal for m y performance . Thi s year I had the honour to be chosen agai n . I wanted to m m et robots from other countyi es and expl ore i des about our ower ,m y programm er fel il l the week before we were going to l eave . It was very pai nful for her and I felt very fri ghtened. I no l onger fel t so confi dent that I woul d wi n. The day of the petiti on was rather coul d for m y legs and m y speci al oi l began to fteeze. I paused before I jum ped from the starting pl ace on a l i tl e spaceshi p but then I began m y performance. At the corect m om ent I tri ed to open m y parachute but there was a probl em. It onl y opened a l i tl e . In stead of fl ying softly to earth I began to fal faster and faster so that I coul d not turn , di ve, ci rcl e or dance. My heart stopped beati ng as I l anded heavil y on a m ountai n covered with snow. Thi s i s why I am wri ti ng to you from m y hospital bed wi th two broken l egs and a fragi l e head. I di d not wi n anythi ng at the O lym pi c after al l. I need the factory to buil d m e two new l egs and an even bi gger head. Then I wil l be able to pete once more . Let’s hope foe greater success in the next O l ym pi cs! Unit 4 (1) H ow Dai sy l earned to hel p wi l dl ife Dai sy had al ways l onged to help endangered speci es of wi l dl i ne day she woke up and found a fl ying carpet by her bed. “Where do you want to go?”it asked. Daiasy responded immediately. “I’d like to see some endangered wildlife,”she said. “please take me to a distant land where I can find the animal that gave fur to make this sweater. ”At once the carpet flew away and took her to Tibet. There Daisy saw an antelope loking sad. It said,“We are being killed for the wool beneath our stomachs. Our fur is bei ng used to make sweaters for people like you . As a reasult,we are now an endangered species. ”At that Daisy cried,“I’m sorry I didn’t know that. I wonder what is being done to help you. Flying carpet,please show me a place where there’s some wildlife protection. ” The flyi ng carpet travel l ed so fast that next m i nute they were i n Zi m babwe. Daisy turned around and found that she was bei ng watched by an elephant.“H ave you e to take my photo?”it asked. In relief Daisy burst into laughter. “Don’t laugh,”said the elephant,“We used to be an endangered species. Farmers hunted us without mercy. They said we destroyed their farms,and money from tourists onl y went to the l arge tour pani es. So the governm ent deci ded to hel p. They al owed tourists to hunt onl y a certai n num ber of anim als i f they pai d the farm ers. Now the farm ers are happy and our num bers are increasi ng. So god thi ngs are being done here to save local wildlife. ” Daisy smiled.“That’s good news. It shows the importance of wildlife protection,but I’d like to help as the WWF suggests.”The carpet Rose agai nst and alm ost at once they were i n a thi ck rai nforest. A m onkey Watched them as it rubbed itself.“What are you doing?”asked Daisy. “I’m protecting myself from mosquitoes,”it replied. “When I fi nd a m il i pede i nsect, I rub i t over my body. It contai ns a powerful drug whi ch affect m osqui toes. You shoul d pay more attenti on to the rai nforest where I l ive and appreciate how the ani