问题 解答题

已知集合A={x|x=m2-n2,m∈Z,n∈Z}.求证:

(1)3∈A;    

(2)偶数4k-2(k∈Z)不属于A.

答案

(1)∵3=22-12,3∈A;

(2)设4k-2∈A,则存在m,n∈Z,使4k-2=m2-n2=(m+n)(m-n)成立,

1、当m,n同奇或同偶时,m-n,m+n均为偶数,

∴(m-n)(m+n)为4的倍数,与4k-2不是4的倍数矛盾.

2、当m,n一奇,一偶时,m-n,m+n均为奇数,

∴(m-n)(m+n)为奇数,与4k-2是偶数矛盾.

综上4k-2∉A.

完形填空

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第二节完型填空(共15小题;每小题1分,满分15分)

Once upon a time,a man punished his 5-year-old daughter for  31  up the family's only roll of expensive gold wrapping paper. Money was tight and he became even more  32  when on Christmas Eve,he saw that the child had pasted the gold paper so as to  33  a shoe box to put under the Christmas tree.

Nevertheless, the next morning the little girl, filled with excitement, brought the gift box to her father and said, “This is for you,Daddy!”Hearing this,the father was  34 by his earlier conversation. But when he opened it, he found it was  35  and again his anger expanded. “Don’t you know, young lady,” he said   36 ,“when you give someone a present there’s supposed to be something inside the package !”

The little girl looked up at him  37  tears rolling from her eyes and said: “Daddy, it’s not empty. I blew kisses into it until it was all full.”

The father was deeply moved. He  38  on his knees and put his arms around his precious little girl. He begged her to  39   him .

An accident  40  the life of the child only a short time later and  41  is told that the father kept that little gold box by his bed for all the years of his life. And  42  he was discouraged or faced difficult problems he  43   open the box,take out an imaginary kiss, and  44  the love of this beautiful child who had put it there.

In a very real sense, each of us as human beings have been given an unseen golden box 45   with unconditional 1ove and kisses from our children, family, friends and God.                  

36. A. doing      B. cutting          C. tearing             D. using

37. A. worried          B. shocked      C. bored         D. terrified

38. A. paint       B. tie         C. decorate        D. hang

39. A. bothered      B. moved          C. embarrassed       D. annoyed

40. A. empty      B. ugly       C. overfilled      D. expensive

41. A. politely    B. angrily          C. thoughtfully      D. eagerly

42. A. in         B. down     C. with           D. for

43. A. 1ay         B. fell        C. rose           D. went

44. A. punish     B. blame     C. forgive          D. beat

45. A. took        B. risked     C. cost           D. destroyed

46. A. this         B. it         C. she            D. he

47. A. whichever    B. whatever    C. wherever       D. whenever

48. A. could       B. should     C. would         D. might

49. A. imagine          B. remember   C. miss           D. find

50. A. put       B. carried          C. covered         D. filled

填空题