Example

c"qa

89-195

siy .'b 'texte qilebxn .q 'text ,

dcica dwihnzn

g"qyz ,'` xhqnq ,'` cren

.ivge miizry :ogand onf .qik oeaygna ynzydl xzen .xfr xnega ynzydl xeq` .daeyz lk aihid wnpl yi .zel`y lk lr zeprl ulnen

(zecewp 28) miqgie zeivwpet ,zeveaw

z` i/`vn ,

C = {c, d, f, g} B = {b, c, e, f } A = {a, b, c, d} D = (A \ B) × (C \ B) ,

,

m` .(zecewp 6)

.1

m` .(zecewp 10)

.2

.

:

? (dnvrl

S

oia miqgi xnelk)

S

S = {a, b, c}

lr yi mipey miix`pia miqgi dnk .(zecewp 2)

(`)

? miixhniq md miqgi dnk ,dl` jezn .(zecewp 2)

(a)

? miixhniq ihp` mbe miixhniq mb mdy

-niqihp` mbe miixhniq mb mdy mixai`

n

S

lr yi miqgi dnk .(zecewp 3)

mr dveaw lr yi miqgi dnk .(zecewp 3)

(b)

(c)

? miixh

.(zecewp 12)

,

g:B→C f :A→B ,

zeivwpet lkle

.lr gxkda dppi`

jk

g:B→C

-e

f :A→B

f

A, B, C

zeveaw lkly i/gked

la` ,lr gxkda `id

zeivwpete .lr dppi`

A, B, C f

g

.(zecewp 6)

if` ,lr `id

g◦f

g

la` ,lre 1-1 `id

g◦f

(`)

m`

zeveaw ly dnbec `vn .(zecewp 6)

-e 1-1 dppi`

.3

(a)

-y

(zecewp 28) zeiqxewxe divwecp`

diqxewxd z` i/xezt .(zecewp 8)

n≥1

xn+1 = xn + 6xn−1 , .

n≥1

,

.4

x 1 = 1 x0 = 2 ,

dlgzd ii`pz mr

irah xtqn lkly divwecp` ici lr i/gked .(zecewp 8)

.5

√ 1 1 1 1 √ + √ + √ + ... + √ ≥ n n 1 2 3

,zeveaw-zz

m

-l mixai`

n

zlra dveaw ly zewelgd xtqn `ed

pm (n)

m` .(zecewp 12) -y i/gked

pm (n + 1) = mpm (n) + pm−1 (n) ,cgiay

jk

,ef

diqxewxl

(mini`zn

pm (n)

.

dlgzd

ii`pz

e`)

mi`zn

dlgzd

i`pz

i/`vn

ly ziaihpxhl` dxcbd miwtqn dlgzdd i`pze diqxewxd

.6

(zecewp 28) dwixehpianew

cg` zegtl ici lr (zix`y `ll) dwelgl mipzip 6000 cr 1-n minlydn dnk .(zecewp 8)

.7

? 7 e` 5 ,2-n

e`

zedfd z` zixehpianew dhiya



n+1 r+1



r r

 

=



+

r+1 r

e`

zixabl` dhiya





+

n≥r

.

r+2 r





+ ... +

i/gked .(zecewp 8)

n r

.8



mr miilily-`l minly md

r

-e

n

o`k

bef lk oiay jk mi'3 dynge mi'2 dyng ,mi'1 dyng obx`l ozip mikxc dnka .(zecewp 12)

.9

? cg` 3-e cg` 2 zegtl yi mi'1 ly

zexazqd" ly avn gipdl yi ,zxg` oiev ok m` `l` ,ze`ad zel`ya

(zecewp 28) zexazqd

.zixyt` d`vez lkl zexazqd dze` yi zi`xw` dxigaa xnelk - "dcig`/ziqlw

,mipal mdn 3 ,miexck 6 liknd ckn mixeck 3 (dxfgd ila) i`xw`a mi`iven .(zecewp 6)

.10

? rav lkn cg` xeck `ivedl zexazqdd idn .mec` 1-e mixegy 2

zexazqdd miyp`

ly

idn

d

.

zebefd

-l

1

oia

xtqn

mly

ly

xtqn

zlgezd

i`xw`a

idn

?

cg`

xtqn

lk

eze`

mixgea exgai

miyp`

n

miitivtq

.(zecewp miyp`

10)

.11

ipyy

? xtqn eze` mixgeay ,xtqn eze` mixgeay zebefd xtqnl 3 mxez df ,xtqn eze` mixgea miyp` 3 m` :dxrd) mxez df xtqn eze` exgay miyp` 4 yi m` oke .miyp` 3-n xagl ozipy zebef 3 yie zeid ('eke .zebefd xtqnl 6

.80

cr

1-n

mipey

mixtqn

8

i`xw`a

xgea

owgyd

,miieqn

ehel

wgyna

.(zecewp

12)

1-n i`xw`a exgapy ,mipey mixtqn 20 ly dniyx znqxtn eheld zxag ,wgynd seqa 5

zegtl

xga

m`

e`

,dniyxay

xtqn

s`

xga

`l

m`

e`

qxta

dkef

owgyd

.80

cr

.dniyxay mixtqn

? dniyxay xtqn s` xegal `l owgyl zexazqdd idn .(zecewp 4)

(`)

? dniyxay mixtqn 7 xegal owgyl zexazqdd idn .(zecewp 4)

(a)

zlgezd idn ,xga owgydy dniyxa mixtqnd xtqn z` onqn

X

m` .(zecewp 4) ?

!dglvda

X

ly

(b)

.12