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北京人大附中英语实验班选拔考试,甚至还出现了多道英语

北京人大附中英语实验班选拔考试,甚至还出现了多道英语
北京人大附中英语实验班选拔考试,甚至还出现了多道英语

很多同学喜欢逻辑推理,说明它有神奇魅力。在小升初考试中,逻辑推理题依旧频繁的出现在各重点中学的试卷里,北京人大附中英语实验班选拔考试,甚至还出现了多道英语的奥数逻辑题,所以加强这方面的训练对于我们学生来说依然是十分必要的。 一、逻辑推理的“生命线”:

逻辑推理找矛盾,真假不清暂先定。找矛盾的依据是逻辑推理的四大定律。

⑴同一律。在同一推理过程中,每个概念的含义,每个判断都应从始至终保持一致,不能改变。 ⑵矛盾律。在同一推理过程中,对同一对象的两个互相矛盾的判断,至少有一个是错误的。例如,“这个数大于8”和“这个数小于5”是两个互相矛盾的判断,其中至少有一个是错的,甚至两个都是错的。

⑶排中律。在同一推理过程中,对同一对象的两个恰好相反的判断必有一个是对的,它们不能同时都错。例如“这个数大于8”和“这个数不大于8”是两个恰好相反的判断,其中必有一个是对的,一个是错的。

⑷理由充足律。在一个推理过程中,要确认某一判断是对的或不对的,必须有充足的理由。 二、逻辑推理的几种主要类型:

1.真假命题判断; 2.数值限定推演; 3.列表与对阵图。 某楼住着4个女孩和两个男孩,他们的年龄各不相同,最大的10岁,最小的4岁。最大的男孩比最小的女孩大4岁,最大的女孩比最小的男孩也大4岁。最大的男孩多少岁?

三名学生进行了若干科目的考试,以考得的名次进行记分。考得第一名得分最多,其次是第二名,第三名得分最少。各科都是如此记分。已知甲最后得22分,乙最后得9分,丙也是得9分。并且已知乙英语考试得了第一名,问数学第二是谁?

甲、乙、丙、丁四人对A 先生的藏书数目做了一个估计,甲说:“A 先生500本书”;乙说:“A 先生至少有1000本书”;丙说:“A 先生的书不到2000本”。丁说:“A 先生最少有1本书”,这四个人的估计中,只有一句是对的,问A 先生究竟有多少本书? 例2 逻辑推理

例3 例1

例4

★★★(2006年浙江省小学数学活动课夏令营)

足球世界杯小组赛的每个小组有四个队参加单循环(每两个队之间都踢一场)比赛,每组的前两名可以出线。其积分方法为:每胜一场得3分,平一场得1分,负一场得0分。当两个组的积分相同时,以净胜球数(总进球数减去总失球数的差)的多少来定名次,净胜球多的队排名靠前。已知某队以最低的积分出线了,那么这个队在小组赛中的积分是_____分。

例5

★★★★(小学数学奥林匹克竞赛)

甲、乙、丙三名运动员囊括了全部比赛项目的前三名,他们的总分分别是8,7和17分,甲得了一个第一名,已知各个比赛项目分数相同,且第一名的得分不低于二、三名得分的和,那么比赛共有_____个项目,甲的每项得分分别是_____。

例6

一次数学考试,共六道判断题,考生认为正确的就画“√”,认为错误的就画“×”。记分的方法是:答对一题给2分;不答的给1分;答错的不给分。已知A,B,C,D,E,F,G七人的答案及前六个人的得分记录在表中,请在表中填出G的得分,并简单说明你的思路。

测试题

1.★★★(2006年我爱数学少年夏令营)小明和7个同学一起在教室里,任意两人之间至多下一盘棋。

若这7个同学下棋的盘数各不相同,则小明下棋的盘数是。

2.甲、乙、丙三人,一个总说谎,一个从不说谎,一个有时说谎。有一次谈到他们的职业,甲说:“我是油漆匠,乙是钢琴师,丙是建筑师”;

乙说:“我是医生,丙是警察,你如果问甲,甲会说他是油漆匠”;

丙说:“乙是钢琴师,甲是建筑师,我是警察”。

你知道谁总说谎吗?

3.(奥数网习题库)小赵家的电话号码是一个由五个不同的数字组成的五位数。小张说:“它是84261。”

小王说:“它是26408。”小李说:“它是49280。”小赵告诉他们:“谁说的某一位上的数字与我家电话号码上同一位数字相同,就算谁猜对了这个数字。现在你们每人都猜对了位置不相邻的两个数字。”这个电话号码是。

4.(仁华学校考题)一个店主准备糖果礼物盒,每个盒子包含从F、G、H中选出的两种硬糖和从P、Q、R、S、T中选出的三种软糖,要求下列条件:

⑴G不能与T同时选出来;

⑵P不能与S同时选出来;

⑶Q不能与T同时选出来。

1.如果G被选出来放入盒子,那么下列哪种糖果也肯定被选出来?( )。

A.F B.H C.P D.Q E.S 2.下列哪种糖果肯定在每一盒礼物中都出现?( )。

A.F B.G C.H D.P E.R 3.如果T被选出来放入盒子,那么这个礼物盒中必然下列哪些糖果?( )。

A.F和G B.F和H C.G和H D.P和R E.R和S 4.对于符合要求的一盒糖果,下列哪种替换方法保证替换后的糖果仍然满足所有要求?( )。

A.把S换为P B.把R换为Q C.把R换为S D.把P换为T E.把Q换为T

5.在一次“25分制”的女子排球比赛中,中国队以3:0战胜俄罗斯队。中国队3局的总分为77分,俄罗斯3局的总分为68分,且每一局的比分差不超过4分,3局的比分分别是 : , : , : 。

6.张红因病在家休息了几天,这期间的气候是: 下了8次雨,时间是上午或下午; 当下午下雨时,当天上午是晴天; 有9个下午是晴天; 有13个上午是晴天。

问她一共在家休息了几天?

答案

1.答案:3或4。

设小明的7个同学为了A ~G ,下图是两种符合题意的对阵方法。

G

小明

F

E

D

C

B

A

A

B

C

D

E

F

小明

G

2.答案:根据题意,三个人的特点各不相同,则由此为假设点。

假设甲从不说谎话,那么乙和丙都有正确的陈述,与存在一个总说谎的人的前提矛盾,所以假设错误。

假设丙从不说谎话,出现与上面相同的情况,因此假设错误,从而得出乙是从不说谎话的人,那么三个人的身份就确定了,从而可以断定甲是一直说谎的人。

3.答案:对比他们三人所猜的三个数字,发现除了小张和小李的百位相同外,其余都不相同。也就是说,其余数位只能一个猜对,共五位,每人对两位,必有两个猜对同一位,只能是小张

和小李同时猜对百位的数字2。

从而知,个位要么是小张对,要么是小李对。

如果小张对,个位是1,则:有小李必对首位是4,而小王的两位中,必有一4与小李重复,与题意五位数字各不相同矛盾。

则必是小李对,个位是0,则首位小张必对,是8,而小王猜对的必是除小李小张三位以外

的两位。所以得:46201。

4.答案:1.D 2.E 3.B 4.A

5.答案:因为77=25×3+2,所以中国队的得分分别是25、25、27。从而俄罗斯必有一场得分为25,另两场得分和为68-25=43,又另两场每场得分均不少于21分,则另两场的得分应分别为

21分,22分,因此3局的比分分别是25:21,25:22,27:25。

6.答案:在8次下雨中,设有x次是上午,则有8-x次是下午。

分别考虑上午、下午。

上午x次雨,13次晴;下午8-x次雨,9次晴。

而上午和下午是一对一的,总数应相等,所以得:

x+13=8-x+9

解得x=2。

因而她共休息了2+13=15(天)。

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