1966-08-19 — Page 13

圖初月七—

英中F.1英文先修專欄。方阄·

'penaon_20

Agreement of the Verb with the Subject

The verb should agree with the subject in number and]

pereon.(動詞漤典主語的影友~精想配合了

(*) A várb must be in the same number and the same person as ital

suhject r

8

1. Tom is reading in the library.f

2. They are playing football...

3. She has taught English sincs 1957,

d. I am very tired.

5. We analLate ondays.

Two or more singular subjects connected by and should take a veh in the plural (and v tk sẻ vɔ ý về A GĦALLI ** **'

1. Jam and Paul have finished their work."

2. Mr. Wong and Miss Lee are good teachers.

3. Two and four make six.

4. Jane and John were invited to the dinner,

5. Tom and May were absent yesterday.

(6) Two singular subjects connected by and, exprassing one idea,

#hould take a verb in the singular: (and

1. Hread and butter is wholesome food."

2. Truth and honasty is the eat poldoy.

3. Slow and steady wins the race.

Al Trail and error is the source of our

knowledge.

(5. Every hour and avery minute is important.

al' a singular subject with attached phrases introduced by with

E

or like or as well as should take a verb in the singular

keewingula

neither

(Welther

1. The old man, with his son, has lived here"

for ten years.

12. Henry, with his friend, is now travelling "on

musiness.

beter, like his rather, is a Mr. Chan. like Mv, Ewenny, is e

artre company

seun ortaman J

en esentativa}

9% old woman, weli as the milkman, was

ktocked gown by the car.

......

UMA

mubjects colinected by mither

no: **60 a vern in the singular i

Dither wary or Jana pas argos mil eng Lither the tiger or the linn xás killeg

the faster.

Bither hear i an night.

4. Reliner Jane nor Mary: poen, to school.

5. Neither gun nor sword was found in the

6. Neither Henry nor Peter was punished.

(7) The singular munjest preceded by each or every takes a

verb in the singular (heach 4 every LA WEB. 1141784 U

1. Each boy has his own pen.

2. Each pupil was punished.

3. Every child nas esten an appis

4. Every minute is important.

pluzs, subject is preceded by one of, each of, either of neither of, every one of, or not one of, the verb in singular 1 14 4A-une of each of either of neither of every one pinot one of fi 80 4 38 18,43 h fla

Exercise 42

vie aj the children has finished the work.

2. One of the niliwe nas katroved

4. Fach of that has been infirmed.

4. fach to the garis like

5. Either y the thieves was caught

6. Bether we the shipa wa sinking»,

7. Nesther of them was very tall.

9. Every one of you has a dictionary.

ile Naths of the passengera, vas hurt

_of_the_twaobore liken Maay,

Underline the wrrect word in the bracketa a

(a) Mary, like her friend, (is, are) willing tờ gi

(*) Bither. Mary or Jane (was, were) caught by the teachers]

(a) Une or than (waa, were) mac by wr, Lae...

((*) Mary and Peter (was, vera) travelling around the world.

(=) Fach man (haa, have) failed in the examination.

(B) Neither of then (has, have) to go to work. (g) My brother, like George, (is, äve) very talas (1) Every little girl (desire, deviras) a nice dolių, (1) Each of the boys (15, are) going on, holiday. (3) The officer and his servants (was, were) workings (x) Pater, as well as John, funs were) given a priz (1) Not one of the boys (125, were) working. Answers to Exercise 41

[{2} vhet gung wants - object of the verb can guess!",... (b) That laha nieda.... object as the wowb. wmata', (o) that she was able to come - object of the verb 'knew, (d) he would do that – 'object

* warb 'uished', {f} when I should come – object of the

object of the

(#) that she failed in the examination →

(h) that he had made a mistake. – object of the bow it happened – object of the

found aski

WAH KID YAT PO

·邀請參斯縠,人

水八四面融氏

一座生,如未河歙

一歲,以上及格價

林孔

港各瓜超商午型餅超營執行香 九峰際

支,半煲 座禮

王院小學.

病會者及格者,藉」 今畢業禮

或晚

申號名慈

小 格助瀾年益

始干雏崋

「蘇氏宗鵡會,定八月

俯贸柞濙博士致詞

《國際肶)愛進歲至十五歲就数小半

獎學聯歡大會

香港教師會與私校協進會合辦

現代數學虐,請在訓講師主喬什枣等鋪 筆錄 狂岳峰 If of (det Theory)

§4 笛卡兒來積間係及序對fcarlesian Product

Relations and Orders Pairs)

誰都知道,歐民平面上每一奌P均可表為P(x,y)其中 手巧為复數,並且,一般地說,奌P(x,y)典奌Q(x,y)是不同的。 除非x=y下面我們把此 概念推廣至任意元素上 定義4-17 由二個对象?和的组成的序对記為(日)被 .確定為如下的集 (a, b) = {{a}, {ab}}

期每

·可向李炳紀念學校該會接洽·世父母。毎年七月十,史道平,張能毅, 再與大家講講大勝至 生佛念同,佛念衆生

內多利亞聯鬱就興中沓會合辦之第二屆「文菡難民」,定十

展品琳瑯滿目歡迎各界參觀

之股,對俊秀之 做良而家境,,供佛及,以報站 英,東湖,潘智聞 菩薩,及大阿羅漢,至今出,佛與來生, 《特朗•九醌焙·家庭又無力供蹤者, 紅日,常以米紫億折 陳道界,麥雅音,發言郎念佛圓通章。按,衆生念佛,如基 女将向有助學金及中璞在學中之品,一生父母,爲作監督徒敬,孫榮,孫道 楞嚴法會:佛問躇大 至從受生那一天,以上命中五時 母豬愛之恩。現在之,陳道化,世道讯,最初發心修星從那一同於形影,且如影蔻、劇本、俗法、威賽、西洋畫、漫盤、閔案查、咸、特、新時,

「五日,《西风冷無证商,為許前萬,而子,法門我方便,得經形,不相離低。如此黑白攝影、彩色攝影、彩色灯熄片、金石、樂曲、雕塑等十人以

:「區」,在膠有助學

下年度結會之中與國中熱還,設於簡報道

傳,故有舉辦之二葛斯马老六月十二五十三位器應)饰進駐大熊心軟線豪生,一下午六時。新迎Q說。 之父母遁入天散光靜君,梁榮年,李蘊良誦者。爾時,大至佛畢竟不二,故錚外,尙有李賴佑醫生激作廢及名家邀請國,数瑯滿目,美不勝收 。鬃老普閱衆生多多 势,易性栽居士等。至法王子,與其同袍 想必經見佛:沉顯具。歷期至廿四日,一連六天,毎日及阿時間,由上午十一霞、區、

| 氏宗親會定期 優良•巴考到中學, 湖內

並且a和长分别精笃序对(al)的第一、第二坐標(The First and The Second Coordinates)

由此定義,立即看到ab,則序对(ab)由單元素. 我组成的集:差,則序对便由二個不同的元{0}和 {a}形组成的集

74.1 (a,b) = (c, d) bs à 3 44 £ a=c fn b=d. (証)必要性团(a,b)=={c,d).則 {{a},{a,l}}={{c},{cd}}

現在我們分如下两种情况加以討論:

(1)若 {a}={c}和{al}={ed} 則 a=c 和f=d} (2){a}={ed}和{ab}={c},則a=c=dw

a = l = c 11⁄2t no a=c, ko bod

-

分性

{c}={e} x_{Q}={d}^{al}={cid}

從而{{a},{ob}} = {{c}{ed}} Bq_(e:b)=(c, d), 定

#4B第二相集,則下列的其

-[(a. b): ac A.. fa Bl

A和B的笛卡兒妻積

(例#1)設 A={1.2}; B={-1.0.3} 則

A+B=

= { (1,-1), (1,0), (1,3), (2-1), (2,0), (2,3)}

AxB=中的-

要條件是中或社

(2) Ax B, C Aax B.的-

要條件是A.CA和BCBa

(3)A,48q=A×B,的-

要條件是A=A和BB 讀者可自行証明之。

124-3(1) AX (BOC)—=== (A»B) N (A¥L

(a)

(3) (AXI

́(4)(A‚×B,)~{A, B,)

← (REA) A (PEB) A (LIC)

AXB)V (AxC)

(A ̧n\A)× (8, n B,)} 8,−B1)] U [ {A,— A‚} xB] (BnB}] v [ Ajx (Bre)]

↔ [(REA) A (LEB)] ^ [ ELEA) ^ (BEC) ← [(a, b) e AxB] ^ [(ab) e A×C] ← (a, b) E (AxB) n (A×C)

••_ Ax (BDC)=(AxB} n ( Ax C)

V (a, b) € A × (BUC) — (a©A) A ( lè BUC),

⇒ (Q&A) A{(&&B)v(BEC)

←>(REA)N(DEB)} V [(a€A}}\(£€C}}

•[cale Ax B] v [cal)¢ AxC] ←> (4L) € (A×B]U (A*C),

* Ax (BUC)= (A×B)u (AxC)

(3) (a, b) € (A,x B) A (A ̧¢ 8.)— [(a, b) & Aa®] ^ [(at)¢ Â×B]

Ba

↔(REA)MEDE B1)] ^ [ (α € A.} A (8 6)

↔ (QE ANAs) NC&BnB⇔a, Bre (An AuJu (BnBu}}

•· (Â‚× B‚ ) Îî ( A‚× B1) = { A‚n A2)× ( 8,78.),

(4)類似地可証明之,由讀者完成

定義3 由序时组成的集R稱為闳係(Relation),並且下

A=fa: Ib.z. (a,b)£R)

B= -{b: Jag (a,b)ER}

分别稱為閩係R 的定義域典值域,並記以dom R和LawR.

(附註)(1)若凡是一間係,顯然地有RC (dom R}x(ren R) (2)若凡是一間係,有時吠ARB呔表式(0.老GR.

(3)关R是一間係,而且_R=中,則稱它為空間係(Emp

Relation).

(4)設工是一集,R是一間係,希dom RCX 和hanRex,則

則△扬蔫来積集区中的对角线(diagonal)或科馬 工中的恒等關係。

定義:4.4]設R和S笃又中的两但間侄

下列関係

SoR={(x,y); x,y¢X, 3z£X •»• (x, z)ER 4T (3.4)Z_S}

特弟R和S的複合間係

(2) R"={(x,y); (y,x) ER, "y€X} fĄ AR WILL MAKE

【定理 小玥话 RST為工中的間係,ᅀ為X牛的恒等関係

QJ (1) To(S»R}={T@S}OR

14 ☆ AM DELL M1A B TOSOR

{R} Roa =LOR=R

(3) R‚OR, CS=S, 4- FIR, CS, 4 R.CS)

(4) (R)'=R

(5) (SoRY' = R*S*

(6) A' =

(証):我們

証),其餘部分由讀者完成之

(x,y) ¢ To (SoR) ←→→]z¢X÷v} {x})e{S¢R}4u (3,y} & \??

←3 £*£ 4*] (x,t)eR. (tz)+S 4= {3•y)¢ 7

f

→ a *<x 4g (ut)ER ke (ty)© ToS ↔(xy)&(T«S}@R»

w_ Io[SoB)=(TAS)PR.

然

日九十月八年六六九一媵公年五十五國民慈

國各然變校長

六「作」 九文中學會考交談中文者 六,在英文中學會学初中文合榻之資格不

* 九龍婦女會助學金

「時,憑 法力迴向佛雅入軟倒懸,以解母親之苦難。 一,紀委後,須於八月二十五日成烈前,辩,目窕念者於染日設孟盆,供以百味五茲供佛及估,發母亲解夏之,如有一天露黨爭,

感

無獅子爲

兩家政府中學

華

化

招收中六新生 樂果長老勉衆生

曆之中學六年(文科及理科) 男女學生 公學將招收一九六六至六七年胞有適當資格 《悲訊)金文案中燃及巴習爾官立中 金文泰及巴宫街

盂蘭期勿忘報恩 劉六個月,爲類一百八十天。凡屬四眾佛子,均可,上三味,據此,以念佛 妗伽前排,跳神好過 倂錄樂老觀音成道日開示語,其最後佛名類日 把!母酒是我類說,湘,常將阿鼻奈生, 佔性對旁坚果長老,由機密公月初一起,建怠佛道堪,一 月光。彼佛苦我念佛 溶仔之凡爾王來報,孀甜,齒機黨, 插不開發此地。汉语 聞性精舍啓建念佛道場六月,以後又回程十二子在他方官司,故佛大米,方鐵法請點, 世,名無愛光,朗森此合前檢,想無益 「沙湖慈海放盡之時間 此您母親在家想子,一世間滿念發切者, 古佛。當時鷸際念,執日聽馆何形,故者,鐵 蔡國見佛,阿佛受法 ,在那碎憫,有佛出而于在外不察母親。食過於母,然子若生成熟,於限定中見佛 侧食,我僚往眥俊河 沿油症,雖泡何用?獲現神。交光大師云佛皆可。爲念佛功夫 座起實證佛足,而白眾生,如母管子,于此合的喩, 箜想必念六字佛,陳念四字 用?娑婆衆生,望 快見佛 · 牌如母于,而功夫成熱,决定 苦無珌,故盤佛念 不相違,作佛也。若專訊念佛 [佛悬出并有十方念佛,佛念亲生,現前常來,必定點

•佛念衆生,风過雄一命茲時見佛,成生衝

「來,都是醫心,個產,他將垌念,原本不第,意味考恩慈阿嬌湯已成書,如以近佈 西方怒姬世界阿彌陀1日,這必相屬,此象,著有辭中,憶佛念傅氣。譬如以近蓉效, ,我夢中尼佛,國

吳昌碩隸書

八廿二日起隔出大渡中供古梵要葛 》

題吳伯憲書群虎

*意州人去佛不結者

今夏條 第二屆文藝叢展

今起接受申請

哀哀父母 我勞,個弟 日均可參加! 子作孝親者,牾念念日常不斷在堪念佛 【 中空懷父母,乃至七 有安法師,李常平 各界愛心參佛當價,日開示語錄列下, 百八十天急停道摄。一九日觀世僧菩睹成

護法

若二人相億者,以其 居士,今天

坐不知命, 一人東莒億准,尉戴著 道

以此單想我

今在大會堂揭幕

鄧石如禄祺四屏之一件 C#二日起展出大進中護古意寫麦)

Ļ若來,

此

중