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Дискретная математика: Графы

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eaeaioiinoe;

a) iao?eoeo aania.

ae) Aeey a?aoa Gi? auienaoue iao?eoeo niaaeiinoe.

Ioia?aoeey aa?oei – ni. ?en 1

a) V={0,1,2,3,4,5,6,7,8,9}

X={{0,1},{0,2},{0,3},{1,2},{1,4},{1,5},{1,6},{1,7},{2,3},{2,5},{3,8},{3
,9},{4,5},{4,6},{5,3},{5,6},{5,8},{6,9},{7,8},{7,9},{8,9}}

A aeaeueiaeoai ?aa?a aoaeoo iaicia/aoueny iiia?aie a oeacaiiii ii?yaeea
ia/eiay n ioey.

a) A0={1,2,3};

A1={0,2,4,5,6,7};

A2={0,1,3,5};

A3={0,2,5,8,9};

A4={1,5,6};

A5={1,2,3,4,6,8};

A6={1,4,5,9};

A7={1,8,9};

A8={1,3,5,7,9};

A9={3,6,7,8};

a) Ioia?aoeey aa?oei e ?aaa? niioaaonoaaiii i. a)

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a) Iieacaia aa?oiyy iieiaeia iao?eoeu, o.e. iao?eoea aania
iai?eaioe?iaaiiiai a?aoa neiiao?e/ia ioiineoaeueii aeaaiie aeeaaiiaee.

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

1

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

ae) Iao?eoea niaaeiinoe aeey a?aoa Gi?.

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

-1

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

1

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

Caaea/a 2 Iaeoe aeeaiao? D(G), ?aaeeon R(G), eiee/anoai oeaio?ia Z(G)
aeey a?aoa G ; oeacaoue aa?oeiu, yaeythueany oeaio?aie a?aoa G.

D(G)=2

R(G)=2

Z(G)=10

Ana aa?oeiu a?aoa G(V,X) yaeythony oeaio?aie.

Caaea/a 3 Ia?aioia?iaaoue aa?oeiu a?aoa G, eniieuecoy aeai?eoiu:

a) “iienea a aeoaeio”;

a) “iienea a oe?eio”.

Enoiaeiay aa?oeia – SYMBOL 97 \f “Symbol” .

a)

a)

Caaea/a 4 Eniieuecoy aeai?eoi I?eia iaeoe inoia ieieiaeueiiai aana
a?aoa G. auienaoue eiae oeeaaeee ia ieineinoe iaeaeaiiiai aea?aaa,
i?eiya ca ei?iaaoth aa?oeio SYMBOL 97 \f “Symbol” .

Aan iaeaeaiiiai aea?aaa – 14.

Eiae oeeaaeee aea?aaa: 000011000001111111.

Caaea/a 5 Eniieuecoy aeai?eoi Aeaeeno?a iaeoe aea?ai e?ao/aeoeo iooae
ec aa?oeiu SYMBOL 97 \f “Symbol” a?aoa G.

Aan iaeaeaiiiai iooe – 8.

Caaea/a 6 Eniieuecoy aeai?eoi Oi?aea – Oaeea?niia, iaeoe iaeneiaeueiue
iioie ai acaaoaiiie aeaoiiethniie i?eaioe?iaaiiie naoe {Gi? , SYMBOL 97
\f “Symbol” , w}. Oeacaoue ?ac?ac ieieiaeueiiai aana.

Iineaaeiaaoaeueiinoue ianuuaiey naoe (ianuuaiiua ?aa?a ioia/aiu
e?oaea/eaie):

1-e oaa

2-e oaa

3-e oaa

4-e oaa

5-e oaa

6-e oaa

7-e oaa

Ieii/aoaeueii eiaai:

Eae aeaeii ec ?enoiea, ?aa?a {6,9},{7,9},{3,9}, ieoathuea aa?oeio
SYMBOL 119 \f “GreekMathSymbols” , ianuuaiiu, a inoaaoaany ?aa?i {8,9},
ieoathuaany io aa?oeiu 8, ia iiaeao iieo/eoue aieueoaa cia/aiea aaniaie
ooieoeee, oae eae ianuuaiiu ana ?aa?a, ieoathuea aa?oeio 8. Ae?oaeie
neiaaie – anee ioa?ineoue ana ianuuaiiua ?aa?a, oi aa?oeia SYMBOL 119
\f “GreekMathSymbols” iaaeinoeaeeia, /oi yaeyaony i?eciaeii
iaeneiaeueiiai iioiea a naoe.

Iaeneiaeueiue iioie a naoe ?aaai 12.

Ieieiaeueiue ?ac?ac naoe ii /eneo ?aaa?: {{0,1},{0,2},{0,3}}. Aai
i?iioneiay niiniaiinoue ?aaia 16

Ieieiaeueiue ?ac?ac naoe ii i?iioneiie niiniaiinoe: {{6,9}, {7,9},
{3,9}, {3,8}, {5,8}, {7,8}}. Aai i?iioneiay niiniaiinoue ?aaia 12.

Caaea/a 7 (Caaea/a i ii/oaeueiia) Auienaoue noaiaiioth
iineaaeiaaoaeueiinoue aa?oei a?aoa G.

a) Oeacaoue a a?aoa G Yeea?iao oeaiue. Anee oaeiaie oeaie ia nouanoaoao,
oi a a?aoa G aeiaaaeoue iaeiaiueoaa /enei ?aaa? oaeei ia?acii, /oiau a
iiaii a?aoa iiaeii auei oeacaoue Yeea?iao oeaiue.

a) Oeacaoue a a?aoa G Yeea?ia oeeee. Anee oaeiai oeeeea ia nouanoaoao,
oi a a?aoa G aeiaaaeoue iaeiaiueoaa /enei ?aaa? oaeei ia?acii, /oiau a
iiaii a?aoa iiaeii auei oeacaoue Yeea?ia oeeee.

Noaiaiiay iineaaeiaaoaeueiinoue aa?oei a?aoa G:

(3,6,4,5,3,6,4,3,4,4)

a) Aeey nouanoaiaaiey Yeea?iaie oeaie aeiionoeii oieueei aeaa aa?oeiu n
ia/aoiuie noaiaiyie, iiyoiio iaiaoiaeeii aeiaaaeoue iaeii ?aa?i, neaaeai
iaaeaeo aa?oeiaie 4 e 7.

Iieo/aiiay Yeea?iaa oeaiue:
0,3,2,0,1,2,5,1,4,5,6,1,7,4,6,9,7,8,9,3,8,5,3.

Noaia Yeea?iaie oeaie (aeiaaaeaiiia ?aa?i iieacaii ioieoe?ii):

a) Aiaeiae/ii ioieoo a) aeiaaaeyai ?aa?i {3,0}, caiueay Yeea?iao oeaiue
(i?e yoii auiieiyy oneiaea nouanoaiaaiey Yeea?iaa oeeeea – /aoiinoue
noaiaiae anao aa?oei). ?aa?i {3,0} e?aoiia, /oi ia i?ioeai?a/eo
caaeaieth, ii i?e iaiaoiaeeiinoe iiaeii aaanoe ?aa?a {0,7} e {4,3}
aianoi ?aiaa aaaaeaiiuo.

Iieo/aiiue Yeea?ia oeeee:
0,3,2,0,1,2,5,1,4,5,6,1,7,4,6,9,7,8,9,3,8,5,3,0.

Noaia Yeea?iaa oeeeea (aeiaaaeaiiua ?aa?a iieacaiu ioieoe?ii):

Caaea/a 8

a) Oeacaoue a a?aoa Gi? Aaieeueoiiia iooue. Anee oaeie iooue ia
nouanoaoao, oi a a?aoa Gi? eciaieoue i?eaioaoeeth iaeiaiueoaai /enea
?aaa? oaeei ia?acii, /oiau a iiaii a?aoa Aaieeueoiiia iooue iiaeii auei
oeacaoue.

a) Oeacaoue a a?aoa Gi? Aaieeueoiiia oeeee. Anee oaeie oeeee ia
nouanoaoao, oi a a?aoa Gi? eciaieoue i?eaioaoeeth iaeiaiueoaai /enea
?aaa? oaeei ia?acii, /oiau a iiaii a?aoa Aaieeueoiiia oeeee iiaeii auei
oeacaoue.

a) Aaieeueoiiia iooue (?aa?a n eciaiaiiie i?eaioaoeeae iieacaiu
ioieoe?ii):

a) Aaieeueoiiia oeeee (?aa?a n eciaiaiiie i?eaioaoeeae iieacaiu
ioieoe?ii):

. Auiieieoue ?enoiie.

Enoiaeiay oaaeeoea.

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

01

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

01

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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Ae?iaei ii ia?aoiaeo x2-x3:

23 SYMBOL 229 \f “GreekMathSymbols” =14+0=14

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

00

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SYMBOL 165 \f “GreekMathSymbols”

23 SYMBOL 229 \f “GreekMathSymbols” =14+1=15

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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00

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

01

SYMBOL 165 \f “GreekMathSymbols”

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00

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

23. Ae?iaei ii ia?aoiaeo x3-x6:

23E36 SYMBOL 229 \f “GreekMathSymbols” =14+0=14

x1

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

01

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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00

36 SYMBOL 229 \f “GreekMathSymbols” =14+6=20

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

1

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

01

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

07

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SYMBOL 165 \f “GreekMathSymbols”

36. Ae?iaei ii ia?aoiaeo x4-x5:

45 SYMBOL 229 \f “GreekMathSymbols” =14+0=14

x1

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SYMBOL 165 \f “GreekMathSymbols”

1

01

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01

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SYMBOL 165 \f “GreekMathSymbols”

00

45 SYMBOL 229 \f “GreekMathSymbols” =14+1=15

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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45. Ae?iaei ii ia?aoiaeo x5-x1:

51 SYMBOL 229 \f “GreekMathSymbols” =14+1=15

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SYMBOL 165 \f “GreekMathSymbols”

1

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SYMBOL 165 \f “GreekMathSymbols”

00

51 SYMBOL 229 \f “GreekMathSymbols” =14+6=20

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SYMBOL 165 \f “GreekMathSymbols”

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01

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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SYMBOL 165 \f “GreekMathSymbols”

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6

Ieii/aoaeueii eiaai Aaieeueoiiia eiioo?: 2,3,6,4,5,1,2.

I?aaea?aai ?acaeaiee:

Caaea/a 10 (Caaea/a i iacia/aieyo) Aeai iieiue aeaoaeieueiue a?ao Knn n
aa?oeiaie ia?aie aeiee x1, x2,…xn.e aa?oeiaie ae?oaie aeiee y1,
y2,…yn..Aan ?aa?a {xi,yj} caaeaaony yeaiaioaie vij iao?eoeu aania.
Eniieuecoy aaiaa?neee aeai?eoi, iaeoe niaa?oaiiia ia?ini/aoaiea
ieieiaeueiiai (iaeneiaeueiiai aana). Auiieieoue ?enoiie.

Iao?eoea aania aeaoaeieueiiai a?aoa K55 :

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Ia?aue yoai – iieo/aiea ioeae ia ioaeai, o. e. ioee oaea anoue ai anao
no?ie e noieaoeao.

Aoi?ie yoai – iaoiaeaeaiea iieiiai ia?ini/aoaiey.

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O?aoee yoai – iaoiaeaeaiea iaeneiaeueiiai ia?ini/aoaiey.

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X

X

*aoaa?oue yoai – iaoiaeaeaiea ieieiaeueiie iii?u.

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Iyoue yoai – aiciiaeiay ia?anoaiiaea iaeioi?uo ioeae.

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?aoaiea n iaioeaaui cia/aieai. Ia?aoiae ei aoi?iio yoaio.

Iieiia ia?ini/aoaiea:

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7

2

Iaeneiaeueiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

3

0

0

0

0

X

x2

0

6

8

7

5

X

x3

0

0

2

1

1

x4

0

7

6

5

3

x5

0

6

5

7

2

X

X

Ieieiaeueiay iii?a:

y1

y2

y3

y4

y5

x1

3

0

0

0

0

6

x2

0

6

8

7

5

7

x3

0

0

2

1

1

1

x4

0

7

6

5

3

2

x5

0

6

5

7

2

3

4

5

Ia?anoaiiaea ioeae:

y1

y2

y3

y4

y5

x1

3

0

0

0

0

6

x2

0

6

8

7

5

7

x3

0

0

2

1

1

1

x4

0

7

6

5

3

2

x5

0

6

5

7

2

3

4

5

Iieiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

3

0

0

0

0

6

x2

0

6

8

7

5

7

x3

0

0

2

1

1

1

x4

0

7

6

5

3

2

x5

0

6

5

7

2

3

4

5

Iaeneiaeueiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

3

0

0

0

0

X

x2

0

6

8

7

5

x3

0

0

2

1

1

X

x4

0

7

6

5

3

X

x5

0

6

5

7

2

X

X

X

Ieieiaeueiay iii?a:

y1

y2

y3

y4

y5

x1

3

0

0

0

0

x2

0

6

8

7

5

1

x3

0

0

2

1

1

x4

0

7

6

5

3

x5

0

6

5

7

2

2

3

Ia?anoaiiaea ioeae:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

x2

0

4

6

5

3

1

x3

2

0

2

1

1

x4

2

7

6

5

3

x5

0

4

3

5

0

2

3

Iieiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

x2

0

4

6

5

3

x3

2

0

2

1

1

x4

2

7

6

5

3

x5

0

4

3

5

0

Iaeneiaeueiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

X

x2

0

4

6

5

3

X

x3

2

0

2

1

1

X

x4

2

7

6

5

3

x5

0

4

3

5

0

X

X

X

X

X

Ieieiaeueiay iii?a:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

x2

0

4

6

5

3

x3

2

0

2

1

1

x4

2

7

6

5

3

1

x5

0

4

3

5

0

Ia?anoaiiaea ioeae:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

x2

0

4

6

5

3

x3

2

0

2

1

1

x4

0

5

4

3

1

1

x5

0

4

3

5

0

Iieiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

x2

0

4

6

5

3

x3

2

0

2

1

1

x4

0

5

4

3

1

1

x5

0

4

3

5

0

Iaeneiaeueiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

X

x2

0

4

6

5

3

X

x3

2

0

2

1

1

X

x4

0

5

4

3

1

x5

0

4

3

5

0

X

X

X

X

X

Ieieiaeueiay iii?a:

y1

y2

y3

y4

y5

x1

5

0

0

0

0

x2

0

4

6

5

3

3

x3

2

0

2

1

1

x4

0

5

4

3

1

1

x5

0

4

3

5

0

2

Ia?anoaiiaea ioeae:

y1

y2

y3

y4

y5

x1

6

0

0

0

0

x2

0

3

5

4

2

3

x3

3

0

2

1

1

x4

0

4

3

2

0

1

x5

1

4

3

5

0

2

Iieiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

6

0

0

0

0

x2

0

3

5

4

2

3

x3

3

0

2

1

1

x4

0

4

3

2

0

1

x5

1

4

3

5

0

2

Iaeneiaeueiia ia?ini/aoaiea:

y1

y2

y3

y4

y5

x1

6

0

0

0

0

X

x2

0

3

5

4

2

X

x3

3

0

2

1

1

X

x4

0

4

3

2

0

x5

1

4

3

5

0

X

X

X

X

X

Ieieiaeueiay iii?a:

y1

y2

y3

y4

y5

x1

6

0

0

0

0

x2

0

3

5

4

2

4

x3

3

0

2

1

1

x4

0

4

3

2

0

1

x5

1

4

3

5

0

5

2

3

A ?acoeueoaoa eiaai:

y1

y2

y3

y4

y5

x1

6

0

0

0

0

x2

0

1

3

2

2

4

x3

3

0

2

1

1

x4

0

2

1

0

0

1

x5

1

4

3

5

0

5

2

3

Enoiaeiue a?ao

Aan iaeaeaiiiai niaa?oaiiiai ia?ini/aoaiey = 12.

Caaea/a 11 ?aoeoue caaea/o 10, eniieuecoy aeai?eoi aaoaae e a?aieoe
(ioiaeaeanoaea aa?oeiu xi e yj).

Oaaeeoea A (enoiaeiay). No?iee – xi , noieaoeu – yj. SYMBOL 229 \f
“GreekMathSymbols” =0

1

2

3

4

5

1

2

01

03

02

02

2

06

7

9

8

6

3

01

1

3

2

2

4

04

8

7

6

4

5

03

7

6

8

3

Ae?iaei ii ia?aoiaeo x2 – y1:

Oaaeeoea A21 SYMBOL 229 \f “GreekMathSymbols” =0+8=8

2

3

4

5

1

00

02

01

00

3

01

2

1

1

1

4

4

3

2

02

4

5

4

3

5

03

3

21 SYMBOL 229 \f “GreekMathSymbols” =0+6=6

1

2

3

4

5

1

2

01

03

02

00

2

SYMBOL 165 \f “GreekMathSymbols”

1

3

2

01

6

3

01

1

3

2

2

4

04

8

7

6

4

5

03

7

6

8

3

21:

Ae?iaei ii ia?aoiaeo x4 – y1:

21A41 SYMBOL 229 \f “GreekMathSymbols” =6+4=10

2

3

4

5

1

00

02

01

00

2

1

3

2

01

3

01

2

1

1

1

5

4

3

5

03

3

41 SYMBOL 229 \f “GreekMathSymbols” =6+4=10

1

2

3

4

5

1

2

01

03

02

00

2

SYMBOL 165 \f “GreekMathSymbols”

1

3

2

01

3

01

1

3

2

2

4

SYMBOL 165 \f “GreekMathSymbols”

4

3

2

02

4

5

03

7

6

8

3

I?iaeieaeaai ii A21:

Ae?iaei ii ia?aoiaeo x5 – y5:

Oaaeeoea A21A55 SYMBOL 229 \f “GreekMathSymbols” =8+2=10

2

3

4

1

00

01

00

3

01

2

1

4

2

1

01

2

55 SYMBOL 229 \f “GreekMathSymbols” =8+3=11

2

3

4

5

1

00

02

01

00

3

01

2

1

1

4

4

3

2

02

5

1

01

2

SYMBOL 165 \f “GreekMathSymbols”

3

I?iaeieaeaai ii A21A55:

Ae?iaei ii ia?aoiaeo x3 – y2:

Oaaeeoea A21A55A32 SYMBOL 229 \f “GreekMathSymbols” =10+0=10

3

4

1

01

00

4

1

01

Aeaeaa ?aoaiea i/aaeaeii: x1 – y3 e x4 – y4. Yoi ia oaaee/eo ioeaieo.

A eoiaa eiaai niaa?oaiiia ia?ini/aoaiea n ieieiaeueiui aanii:

I?aaea?aai ?acaeaiee:

hSymbols”

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