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Adrian Dușa
Elemente de analiză comparativă
Copyright © 2014 Adrian Dușa
Toate drepturile rezervate, inclusiv dreptul de a reproduce fragmente
din carte.
Colecția Sociologie
Tritonic grup editorial
București, România
Str. Coacăzelor nr. 5
Email: [email protected]
www.tritonic.ro
Descrierea CIP a Bibliotecii Naționale a României
DUȘA, ADRIAN
Elemente de analiză comparativă / Adrian Dușa
București, Tritonic, 2014.
ISBN 978-606-749-004-6
Coperta colecției: Alexandra Bardan
Editor: Bogdan Hrib
Tehnoredactor: Adrian Dușa
Comanda TA1 / octombrie 2014
Bun de tipar: decembrie 2014
Tipărit în România
Orice reproducere, totală sau parțială, a acestei lucrări, fără acordul
scris al autorului, este interzisă și se pedepsește conform Legii
dreptului de autor.
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Adrian Dușa
Elemente de analiză
comparativă
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1 − R2
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±3%
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±3%
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R2
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⇐⇒
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1
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︸ ︷︷ ︸ ︸ ︷︷ ︸
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︸ ︷︷ ︸ ︸ ︷︷ ︸
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tt + 1
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2
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i
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n n − k k
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k k
5
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χ2
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R N
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{a1 a2 . . . an}
x1...n ∈
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µA =
{0 /∈1 ∈
µU
⊂ : { ∈ ⇒ ∈ }
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∅
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3
µA =
⎧⎨
⎩
0121
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{0 =
0n − 1
1n − 1
2n − 1
. . .n − 1n − 1
= 1}
{ }
µSR =
{0 /∈1 ∈
µSG =
{0 /∈1 ∈
µSV =
{0 /∈1 ∈
µS =
⎧⎨
⎩
012
µR(x) =
⎧⎪⎪⎨
⎪⎪⎩
0123
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3 nn
n n
n
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[0, 1]
[0, 1]
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·
····
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∼ ¬
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·
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∪
∩ ·
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·
·
··
·
· ·
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×
rxy = ryx
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⇐
⇐
⇐
⇐
⇐
![Page 133: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/133.jpg)
⇒
![Page 134: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/134.jpg)
⇒
×
×
![Page 135: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/135.jpg)
×
![Page 136: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/136.jpg)
×X ⇐ Y
inclX⇐Y =c
a + c
X ⇐ Y
covX⇐Y =c
c + d
![Page 137: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/137.jpg)
×
P(Y|X) =P(Y ∩ X)
P(X)=
cc + d
inclX⇒Y =c
c + d
covX⇒Y =c
a + c
![Page 138: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/138.jpg)
×
![Page 139: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/139.jpg)
⇐
⇒
![Page 140: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/140.jpg)
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· ⇒⇒ ⇒ ̸⇒ ̸⇒
· · ⇒
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· ⇐
·
·
·
![Page 143: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/143.jpg)
⇒
![Page 144: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/144.jpg)
⇐⇐ ⇐ ̸⇐ ̸⇐
![Page 145: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/145.jpg)
![Page 146: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/146.jpg)
2k k
22 = 423 = 8
![Page 147: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/147.jpg)
![Page 148: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/148.jpg)
2k k
![Page 149: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/149.jpg)
· ·Abc
ABc Abc + ABc
![Page 150: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/150.jpg)
X x X + x
Abc + ABcAc Ac(b + B)(b + B) Ac
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![Page 152: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/152.jpg)
![Page 153: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/153.jpg)
26 = 30
![Page 154: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/154.jpg)
![Page 155: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/155.jpg)
·
![Page 156: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/156.jpg)
··
·
·
![Page 157: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/157.jpg)
![Page 158: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/158.jpg)
![Page 159: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/159.jpg)
1 00 21 01 10 11 20 20 11 0
![Page 160: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/160.jpg)
1
2
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× ×
![Page 162: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/162.jpg)
A{0}B{3}C{0}+ A{1}B{3}C{0}+ A{2}B{3}C{0} ⇒ Y
B{3}C{0} ⇒ Y
A{0}B{3}C{0}+ A{1}B{3}C{0} ⇒ Y
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![Page 164: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/164.jpg)
⇐ ⇒ ⇒
××
![Page 165: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/165.jpg)
×
inclX{1}⇒Y =c
c + d
inclX{2}⇒Y =e
e + f
covX{2}⇒Y =e
a + c + e
inclX{2}⇐Y =e
a + c + e
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covX{2}⇐Y =e
e + f
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![Page 168: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/168.jpg)
![Page 169: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/169.jpg)
![Page 170: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/170.jpg)
![Page 171: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/171.jpg)
¬
−
−
![Page 172: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/172.jpg)
×
·0 · 0 = 00 · 1 = 01 · 0 = 01 · 1 = 1
![Page 173: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/173.jpg)
∩
∩
2 × 2
∪
![Page 174: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/174.jpg)
∪
2 =
![Page 175: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/175.jpg)
√0.4 =
![Page 176: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/176.jpg)
![Page 177: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/177.jpg)
◦ ◦
![Page 178: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/178.jpg)
![Page 179: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/179.jpg)
![Page 180: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/180.jpg)
1 2
1 2
![Page 181: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/181.jpg)
1 2 1
2 1
2
1 2
![Page 182: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/182.jpg)
X ⇐ Y
Xi ≥ Yi
![Page 183: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/183.jpg)
⇐
∑ min(Xi, Yi)
∑ Yi∈ [0, 1]
![Page 184: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/184.jpg)
X ⇒ Y (Xi ≤ Yi)
![Page 185: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/185.jpg)
⇒
∑ min(Xi, Yi)
∑ Xi∈ [0 , 1]
![Page 186: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/186.jpg)
inclX⇐Y =∑ min(Xi, Yi)
∑ Yi
covX⇐Y =∑ min(Xi, Yi)
∑ Xi
![Page 187: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/187.jpg)
inclX⇐Y =c
a + c=
51 + 5
=56
![Page 188: 1 1 £© 19XkXR JmH 'BKB/BbiBM+i2#Bp H2Mi2 XXXXXXXXXXXXX Ry9 9XkXk JmH 'BKB/BbiBM+i2KmHiBp H2Mi2 XXXXXXXXXXX Rye 9XkXj JmH 'BKBp ;B XXXXXXXXXXXXXXXXXXXXX RyN 9Xj PT2` 'BB+mKmH 'BKB](https://reader030.vdocuments.net/reader030/viewer/2022040910/5e84794fc42c8f05cd2195d5/html5/thumbnails/188.jpg)
inclX⇐Y =∑ min(Xi, Yi)
∑ Yi=
56
inclX⇒Y =∑ min(Xi, Yi)
∑ Xi
covX⇒Y =∑ min(Xi, Yi)
∑ Yi
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× ×
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× ×
× ×
×
× ×
23
ck
c k
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c1 × c2 × · · ·× ck
2k k
2k
2 × 2
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− −
−
kk
k 2
k 3
k 4
k k
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2k
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1
2
3
4
5
6
7
8
1 8
3
1
2
3
4
5
6
7
8
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1
inclabC⇒Y =∑ min(abC, Y)
∑ abC=
1.11.9
= 0.579
1
2
3
4
5
6
7
8
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inclaBc⇒Y =∑ min(aBc, Y)
∑ aBc=
1.41.4
= 1.000
1
2
3
4
5
6
7
8
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23 = 8
2 7
3
1
2 7
4 6
5 8
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6
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−−
. . .
. . .
. . .
. . .
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−−
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. . .
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
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8,15
10
11
1
16,17
2,3,6,18
7
9
4
5,13
14
12
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25 = 32
· · · ·· · · ·
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××
××××
× ××
×
C220
C238
C219
5
×
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· ·
·
· ·
·
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