1968-11-28 — Page 22

日八廿月一十年八六九一股公年七十五國民蒂中

By reference to the characteristics of living organism compare the differences between Amoeba SIA SOLIDZYra,

吉九初月十年申戊歷室

WAH KIU YAT PO

1969

高試題演習

CCC英文中學會考

題預習

Ans

現代數學科

生物科

四

廖百琴·

BIOLOGY (

(四)

MODERN MATHEMATICS (4

11. Algebra of data

Concept of date and est terminole

The notion of set: is one of the most

Important and basic concepte, found in mathematics. Without the notion of set various branches of mathematics cannot be unified and integrated, for mathematics, viewed as 1solated facta is not mathematice at all. Moreover, it is the potion of set that has clarified many mathematics which cannot be explained before.

dena in exaa ty

As a description of the idea, it is enough to say: a set is a collection of well-defined objects thought of as a whole. In fact, the notion of a set

is a primitive concept. We cannot declara an exact meaning of asta. That is, the Bermeet can be used to explain many mathematical terms, but it canïot. be defined exactly by other terms. Although:

cannot define a set, we can distinguish Bet from other sets by the common characteristice of ita individuals.

Since a set is a collection of well- defined objects, these objecte may be any entities, concrete or abstract. For example, we may consider a set books or

or a set of pencils, and we may also consider a set of numbers, or a set of points, or a set of ideas.

In order to undertake same operational performancea on sets, we have to know the basic terminology about seta; and learn the operational laws of sete just as we learn the addition and multiplication laws of numbers,”

The basio concept of a set includes the idea that a set is composed of members för elements) and these members belong to the set. We use capital lettera A, B, Ceto, to designate sate. We write acAL to designate that the member a belongs to the set A. We write atA!

-not"

A that the member d does

not la specified by two waysi (1) by listing out all its members (or elements); (ii) by describing the common properties of its members.

Examples

«fxlx 18

natural aumber)

is an English alphabet

Notice that three dots are used to

show that the sequence continues infinitely

or to show that the meubers are too many

be listed.

to

If each member of s eet" à li also

member, or a second set B, then the set

ubset of set by denoted by

AB

If there is at least one element in

3 which is not in, then 4 is a proper subset of B, denoted by.

According to the definitions every

is a subset of itself,

A Bat without any nerber le called

the empty set, denoted by

Bet.

The empty set. § le a subset of avery

If every camber of A is also a member of B. and every member of B la also a member of Al- then à la sonal to 8. That

EB and B), trow = CD

ve base operations on numbers, we

have operations on sets. We have the operations as addition and multiplication on numbers. In these operations we asaign single numbers to pairs of numbers.

Such operations are called binary operations. In dealing with sete, we have two operation6 similar to addition and multiplication. They are the intersection and union of mets, denoted by

AB and AUB respectivaly.

The intersection of two sets A and B or A/13 is the set of all elementa that belong to both A and B.

Example:"

Given A s{ x|x is an odd number}

Bfxx is a prime number

then Anxix la an odd and

prime number

The union of two sets A and 3 or "AUB is the set of all elements that

belong to A or to B or to both.

Example

Given

- fall boys in a school} Ball girla in a school] AUB = All the students in the school

Not all operations on sets are binary Just as not all operations on numbers ard binary. The extracting of the square root of a number and the raising of a number to a certain power are not binary but unary operations. The operation that acts

ΔΟΥ 80€ 18. on a single sat to produce a called a unary operation. Given a set A the set of just these elements in the universe that do not belong to do

called the complement of A, denoted by

A or A. Universe is the set under discussion,

Hence finding the complement of a set is. an unary operation..

nawer to the exercise of last week:

comparison of the differences between Amoeba and Jpfrogyra ·

Amoeba

Spirogyra

Unicellular animal. Milticellular plant,

Holozoic nutrition-Holophytic

Type

leaves of a flowering plant? How does a stem differ from a root?

mist have to take

what are the rain functions or roots, stems, and

Ans. Functions of roots:

1. To absorb water and dissolved mineral salts, such as calcium, phosphorus, sodium, potassium etc. from the soil through the root hairs,

To anchor the body of the plant firmly in tra soil. This is due to the widespreading of roots

3. To act as a passage through which water and.

soluble salts are conducted to the stems and leaves from the regions of absorption.

In many cases the root is modified to serve other purposes, eg. storage, vexetallve propagation and breathing,

Functions of stems:

To serve as a passage for the conduction of water and dissolved onerals from the roots to leaves, and of manufactured food from leaves to other. parts of the body of the plant.

to hold the leaves and flowers to the best advantage so as to obtain maximum amount of sunlight for photosynthesis and best position; for pollination.

To act as a food-storage organ, e.gi the modified stems of ginger, lotus and potato. To, serve for the vegetative propagation,

e.grhizome, tem tuber, corm and bulb

5. The stem sometimes is modified in the of

tendril for climbing.

Functions of leaves

The green leaves contain chlorophyll and can synthesize food by the process of photosynthesis. Leaves possess stomata which serve as the passage for the exchange of gases during photosynthesis and respiration.

To get rid of excess water by means or transpiration.

The leaves sometimes serve for the food-storage; (e.g. the scale leaves of a bulb), and for vegetative ropagation (eg, the leaves or Begonia).

stem differs from a root as followS I

Stea

bears leaves and flowers.

Nodes and internodes ara present.

lip La protected by scale leaves of the terminal tua, Cuticle is present for protection. Usually green (e.z. herbaceous 1.

Lears axillary bud.

Stem hairs are

Root

Meyer bears leaves and flowers,

2. There are no nodes and

internodes,

3. The root tip is.

protected by the root cap.

A There is no presence

of cuticle.

5. Mevar green,

6. pears no axillary bud.

usually multicellular. 7. Root hairs are

Grows above the ground surface and towards the source. of light..

Lylem and phloem. are on same radii

of the plant

atoma la are usually present.

Example:

unicellular,

8. Grows under the ground

surface and goes away from the source of fight

Xylem and pillion are alternate

10. Has do`stomita,

Uzilverse fall residents in H.K.}

A fall female residents in H.K.}

-fall mile residents in H.K.}

Operational laws of seta

To operate on sets we should follow some rules or laws. What follows are the operational laws of sets with the familiar notions, D

U

Operational laws of sets:

LÀW 1. ClosurÚ

·Union (U)

A UB is a set

Commutative ADB, ĐƯA

Intersection AB is a set

ΑΛΒ BAA

(AMB) NC »

Associative (AUB) UC

AV(BUC)

An BNC)

Idempotent AVA PA Identity

ANA

Anu

And

A/ (BUG)

(ASB) UHASTC)

A UU = U

Distributive. AU (BAG)

(KUBISHAUG) Complement, AUA* *

8. De Morgan's (AUB)"

9. Involution

10. Absorption.

LU(A/15)

AЛB

(A/B) · SAVYB'

AN(ANB)

In proving these laws we can only employ thé defined and undefined terms that have been developed. These are the notions of membersmp and nonmembership of a set, and the definations intersection of sats. union of sets, and complement of a set

If two sets A and o are considered, unen, any member x of the universe U falls into exactly of these four categorias 1

Movement

Respiration

Irritability. Excretion.

Cell wall or

membrane

urowth

Dano-

OD

in organic food,

Very active and carries out Locomotion CO2 and 02

exchange through

nutrition

synthesizes organic food from raw materials obtain- ing in water, Passive and carries no locomotion.

The exchange of gases is also.

the body surface by carried out by means of diffusion, diffusion,

Well-developed,

Nitrogenous wastes

are excreted. through the body surface.

Cell membrane is

protoplasmic. membrane.

Hapid and

noticeable

contractile

Not developed...

No nitrogenous

excretion.

The cell is enclosed

by both the

protoplasmic

membrane and cellulose wall.

Inevident.

The presence of the The presence of

vacuole serves to regulate the amount

of water in the body.

Reproduction

inly by a sexual

Exer

means, ï.e. binary fission and sporo. formation:

for this week:

strong cell-wall

prevents more water entering when the call. is turgid.

Both asexual and sexual, i.e. fragmentation and. conjugation.

I. (a) What is photosynthesis? State the conditions

necessary for it to occur.

(b) By what experiments would prove that (1) carbon

dioxide and (fi) Light are essential for photosynthesis?

I write on the line at the right of each statement

or question the number preceding the word or ession that best completes the statement answers the question

1. Most water enters à plant through the

(1) phloem (2) cambium (3) xylem (4) root hair! (5) root cap.

Raspiration in plants releases (1), water

vapour (2) oxygen (3) carbon dioxide

(4) carbohydrate (5) simple sugar. 2.

The tiny opanings in the surfaces of a leaf are the (1) chloroplasts (2) fenticals (3) cuticles (4) stomata (5) micropylas,

32

What are the essential parts of the embry

seed?

in

(1) testa, radicle and plumle, (2) testa, cotyledon and endosperm (3) cotyledon, plumule and radicla. (4) testa, cotyledon, micropyle.

(5) cotyledon, cole optile and coleorhize.

(未完轉入第六張第三

El and £5

x EA and x 28

XEA and x £B

XEA and XEB

Ir three sets A, B, and C are considered). then, x of the universe falls into one of the eight categories, and so on.

Examples:

(1) Prove the Absorption Law, AULAMB)

AU(ANB).

εεεε

i te & å 6

You observe that any element that belongs to A also belongs to.AU (A/B), and any element x which does not belong to. A also does not celeng to A U(A/B), and conversely, Hence AU (A (YBED AL

(2) Prove the De Morgan's Law? (AUB)

છે.

(AUB)

AMEL

& 8 A & E ६.६६

Since the membership table of (A UB), the same as that of A'B'. Hence (AUB)

∙AB!

Problems for the week:

11) Prove the comutative law of the union}

by mambarahis tahlman

(2) Prove the associative law of union by?

membership table.

(3) Frove the identity law of intersection,

by memberahiv table.

Frove the complement law of intersection'

membership table.