專業(yè)好文檔試卷代號：5-5 座位號 中央廣播電視大學(xué) 學(xué)年度第 學(xué)期期末考試計算機(jī)科學(xué)與技術(shù)專業(yè) 級第二學(xué)期離散數(shù)學(xué)試題2009年 7月題號一二三四五六總分得分一、單項選擇題（每小題3分，本題共15分）1若集合A=1，2，1，2，則下列表述正確的是( ) A2A B1AC1A D2 A2已知一棵無向樹T中有8個頂點(diǎn)，4度、3度、2度的分支點(diǎn)各一個，T的樹葉數(shù)為( )A6 B4 C3 D53設(shè)無向圖G的鄰接矩陣為,則G的邊數(shù)為( )A1 B7 C6 D144設(shè)集合A=a，則A的冪集為( )Aa Ba，aC，a D，a5下列公式中 ( )為永真式AAB AB BAB (AB) CAB AB DAB (AB)二、填空題（每小題3分，本題共15分）6命題公式的真值是 7若無向樹T有5個結(jié)點(diǎn)，則T的邊數(shù)為 8設(shè)正則m叉樹的樹葉數(shù)為t，分支數(shù)為i，則(m-1)i= 9設(shè)集合A=1，2上的關(guān)系R<1, 1>,<1, 2>，則在R中僅需加一個元素 ，就可使新得到的關(guān)系為對稱的10("x)(A(x)B(x，z)C(y)中的自由變元有 三、邏輯公式翻譯（每小題6分，本題共12分） 11將語句“今天上課”翻譯成命題公式12將語句“他去操場鍛煉，僅當(dāng)他有時間”翻譯成命題公式 四、判斷說明題（每小題7分，本題共14分）判斷下列各題正誤，并說明理由13設(shè)集合A=1，2，B=3，4，從A到B的關(guān)系為f=<1, 3>，則f是A到B的函數(shù)14設(shè)G是一個有4個結(jié)點(diǎn)10條邊的連通圖，則G為平面圖 五計算題（每小題12分，本題共36分） 15試求出（PQ）（RQ）的析取范式16設(shè)A=1, 1, 2，B= 1, 2，試計算（1）AB （2）AB （3）A -（AB）17圖G=<V, E>，其中V= a, b, c, d ，E= (a, b), (a, c) , (a, d), (b, c), (b, d), (c, d)，對應(yīng)邊的權(quán)值依次為1、2、3、1、4及5，試（1）畫出G的圖形； （2）寫出G的鄰接矩陣；（3）求出G權(quán)最小的生成樹及其權(quán)值六、證明題（本題共8分）18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"If we dont do that it will go on and go on. We have to stop it; we need the courage to do it."His comments came hours after Fifa vice-president Jeffrey Webb - also in London for the FAs celebrations - said he wanted to meet Ivory Coast international Toure to discuss his complaint.CSKA general director Roman Babaev says the matter has been "exaggerated" by the Ivorian and the British media.Blatter, 77, said: "It has been decided by the Fifa congress that it is a nonsense for racism to be dealt with with fines. You can always find money from somebody to pay them."It is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. It is all nonsense."We can do something better to fight racism and discrimination."This is one of the villains we have today in our game. But it is only with harsh sanctions that racism and discrimination can be washed out of football."The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday."I am going to be at the match tomorrow and I have asked to meet Yaya Toure," he told BBC Sport."For me its about how he felt and I would like to speak to him first to find out what his experience was."Uefa hasopened disciplinary proceedings against CSKAfor the "racist behaviour of their fans" duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were "surprised and disappointed" by Toures complaint. In a statement the Russian side added: "We found no racist insults from fans of CSKA."Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).cause there