A:.Β?Φ C.:.?4< B2;ΥΑ2Γ
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1. L2+−∋% 342325−∋−21%/ 4
1.1. I;Α?<1Β006Ω; . . . 4
1.2. !Ω460. I;3<?:.9 . . . 4
1.2.1. AΗ?:.06<;2≅ < E;Β;06.1<≅ . . . 4
1.2.2. ∃=2?.06<;2≅ BΡ≅60.≅ . . . 4
1.3. A942/?. 12 =?<=<≅606<;2≅ . . . 21
1.3.1. !. ?249. 12 ≅Β≅Α6ΑΒ06Ω; . . . 21
1.4. CΒ.;Α6Η0.1<?2≅ . . . 24
1.4.1. ∋249.≅ =.?. 29 Β≅< . . . 28
1.4.2. CΒ.;Α6Η0.1<?2≅ 0<; Χ.?6.≅ Χ.?6./92≅ . . . 33
1.4.3. #24.;1< .Η?:.06<;2≅ 0<; CΒ.;Α6Η0.1<?2≅ . . . 34
1.4.4. #24.;1< .Η?:.06<;2≅ 0<; :Ρ≅ 12 Β; 0Β.;Α6Η0.1<? . . . 35
1.4.5. ∋249.≅ =.?. 29 Β≅< . . . 36
2. CΒ(−+25 : 5−56)0%5 () 170)4%∋−Β1 38 2.1. C<;02=Α< 12 0<16Η0.06Ω; . . . 38
2.2. (6≅Α2:. 12 ;Β:2?.06Ω; 1206:.9 . . . 38
2.3. (6≅Α2:. 12 ;Β:2?.06Ω; /6;.?6. . . 39
2.3.1. C<;Α2< 2; /6;.?6< . . . 39
2.4. (6≅Α2:. 12 ;Β:2?.06Ω; <0Α.9 . . . 41
2.5. (6≅Α2:. 12 ;Β:2?.06Ω; 52Ε.1206:.9 . . . 41
2.6. C<;Χ2?≅6Ω; 2;Α?2 ≅6≅Α2:.≅ 12 ;Β:2?.06Ω; . . . 42
2.6.1. C<;Χ2?≅6Ω; 1206:.9 . /6;.?6< . . . 42
2.6.2. C<;Χ2?≅6Ω; 129 ≅6≅Α2:. 1206:.9 .9 <0Α.9 . . . 43
2.6.3. C<;Χ2?≅6Ω; 2;Α?2 9<≅ ≅6≅Α2:.≅ /6;.?6< Φ <0Α.9 . . . 45
2.6.5. C<;Χ2?≅6Ω; 2;Α?2 9<≅ ≅6≅Α2:.≅ 52Ε.1206:.92≅ Φ /6;.?6< . . . 47
2.7. ∃=2?.06<;2≅ .?6Α:ΤΑ60.≅ 2; 29 ≅6≅Α2:. /6;.?6< . . . 48
2.7.1. (Β:. /6;.?6. . . 48
2.7.2. ∋2≅Α. /6;.?6. . . 49
2.7.3. ∀Β9Α6=960.06Ω; /6;.?6. . . 49
3. C21.71625 50 3.1. D2Η;606<;2≅ BΡ≅60.≅ . . . 50
3.2. ∃=2?.06<;2≅ 2;Α?2 0<;7Β;Α<≅ . . . 50
3.2.1. ∗;6Ω; . . . 50
3.2.2. I;Α2?≅2006Ω; . . . 51
3.2.3. D632?2;06. . . 51
3.2.4. C<:=92:2;Α.?6< . . . 51
3.2.5. D632?2;06. (6:ΤΑ?60. . . 51
3.3. A942/?. 12 0<;7Β;Α<≅ : DΒ.961.1 . . . 51
3.3.1. !2Φ2≅ I12:=<Α2;Α2≅ . . . 52
3.3.2. !2Φ2≅ C<;:ΒΑ.Α6Χ.≅ . . . 52
3.3.3. !2Φ2≅ A≅<06.Α6Χ.≅ . . . 53
3.3.4. !2Φ2≅ D6≅Α?6/ΒΑ6Χ.≅ . . . 54
3.3.5. !2Φ2≅ 12 I12;Α61.1 . . . 54
3.3.6. !2Φ I;Χ<9ΒΑ6Χ. . . 55
3.3.7. !2Φ2≅ 129 C<:=92:2;Α.?6< . . . 56
3.3.8. !2Φ2≅ 12 D2 ∀<?4.; . . . 57
3.4. C<;7Β;Α<≅ Η;6Α<≅, =?6;06=6< 12 0<;Α2< . . . 61
4. N2∋−21)5 52&4) =/+)&4% () B22/) 66 4.1. D2Η;606Ω; 12 Θ942/?. 12 B<<92 . . . 66
4.1.1. %?6;06=6< 12 1Β.961.1 129 Ρ942/?. 12 B<<92 . . . 67
4.1.2. %?<=621.12≅ 2; Β; Ρ942/?. 12 B<<92 . . . 68
4.2. EΕ=?2≅6<;2≅ 12 B<<92: F<?:. ≅Β:. 12 =?<1Β0Α<≅ . . . 69
4.2.1. D2Η;606Ω; 12 :.ΕΑ2?: Φ :6;Α2?: . . . 71
4.3. ∃/Α2;06Ω; 12 9.≅ 3<?:.≅ 0.;Ω;60.≅ . . . 72
4.4. (6:=96Η0.06Ω; 12 3Β;06<;2≅ B<<92.;.≅ . . . 76
4.4.1. E9 :ΤΑ<1< .942/?.60< . . . 76
5. C2037)46%5 LΒ+−∋%5 92
5.1. C<:=Β2?Α. #A#D . . . 93
5.2. C<:=Β2?Α. #∃∋ . . . 93
5.3. C<:=Β2?Α. ,∃∋ . . . 93
1. L2+−∋% 342325−∋−21%/
1.1. I1642(7∋∋−Β1
(2 =Β212 1206?, >Β2 9. 9Ω460. 2≅ 9. 062;06. 12 9<≅ =?6;06=6<≅ 12 6;32?2;06. < ?.Γ<;.:62;Α<≅ 3<?:.9:2;Α2 ΧΡ961<≅. !< 2≅=20ΥΗ0< 12 Β; ?.Γ<;.:62;Α< < 6;32?2;06. 0<;06≅Α2 2; 12?6Χ.? Β;. 0<;09Β≅6Ω; . =.?Α6? 12 Β;.≅ =?2:6≅.≅ ≅64Β62;1< Β;. ?249. 12 6;32?2;06. 1.1., 99.:.1. :<1Β≅ =<;2;≅. D2 2≅Α. 0<;09Β≅6Ω; ≅2 1602 >Β2 2≅ 3<?:.9:2;Α2 ΧΡ961., 2≅ 1206?, >Β2 ≅6 ≅Β≅ =?2:6≅.≅ ≅<; Χ2?1.12?.≅ 2;Α<;02≅ 9. 0<;09Β≅6Ω; Α.:/6Τ; 2≅ Χ2?1.12?.. !. 9Ω460. ≅2 <0Β=. 12 9. Χ.9612Γ 12 9<≅ ?.Γ<;.:62;Α<≅ Φ ;< 12 9. Χ2?1.1 < 3.9≅21.1 12 9<≅ 2;Β;06.1<≅ >Β2 9. 0<:=<;2;.
1.2. LΒ+−∋% I1∗240%/
1.2.1. A<40%∋−21)5 2 E171∋−%(25
A9 =?</.? Α2<?2:.≅ 2; :.Α2:ΡΑ60.≅ 12/2:<≅ 120616? ≅6 062?Α.≅ .Η?:.06<;2≅ ≅<; 062?Α.≅ < ;<. A<40%∋−Β1: E;Α2;12?2:<≅ >Β2 Β;. .Η?:.06Ω; 2≅ .94< (>Β2 2Ε=?2≅.:<≅ 2; 3<?:. <?.9, 2≅0?6Α. < 12 0Β.9>Β62? <Α?. 3<?:.) 12 9<≅ >Β2 ≅2 =Β212 1206? ≅6 2≅ 062?Α< < 3.9≅<.
ΛE∀ ∗ab∀e(% de e)∗e )a∀6∃ e) ,e(deΜ Φ Λe∀ ∗ab∀e(% de∀ )a∀6∃ 19 01 e) b∀a∃c%Μ. A:/.≅ ≅<; .Η?:.06<;2≅. D2 9. =?6:2?. ;< Α2;2:<≅ 1Β1.≅ ≅6 2≅ Χ2?1.12?. < 3.9≅. Φ 12 9. ≅24Β;1. ;< 5.Φ 02?Α2Γ., ≅6; 2:/.?4<, Α.:/6Τ; 2≅ Β;. .Η?:.06Ω; Φ ;< 2≅ ;202≅.?6< 2≅Α.? 2; 9. 0.=.061.1 12 ≅./2? =2?≅<;.9:2;Α2 9. ?2≅=Β2≅Α..
%<? <Α?. =.?Α2, ΛVia a( e∃ ∀a ∃%cheΜ Φ Λ#i(a( ∗e∀e,i)i6∃Μ. #< ≅<; .Η?:.06<;2≅. D2 Τ≅Α.≅ ;< ≅2 =Β212 1206? >Β2 ≅2.; Χ2?1.12?.≅ < 3.9≅.≅.
)<1. .Η?:.06Ω; 2≅ Χ2?1.12?. < 3.9≅. Φ ;< 5.Φ Β;. .Η?:.06Ω; >Β2 ≅2. Χ2?1.12?. Φ 3.9≅. .9 :6≅:< Α62:=<. E≅Α. ≅Β=<≅606Ω; 9. 99.:.:<≅ 9. L): ()/ 6)4∋)42 )9∋/7−(2.
!. :.Φ<?Υ. 12 9<≅ :.Α2:ΡΑ60<≅ 9< .02=Α.;, ≅6; 2:/.?4<, .94Β;<≅ 12:.≅6.1< 3<?:.92≅ ≅2 ?25Β≅.; . Β≅.?9..
∗;. 0<;≅20Β2;06. 12 2≅Α. ≅Β=<≅606Ω; 2≅ >Β2 ≅6 Β;. .Η?:.06Ω; ;< 2≅ 3.9≅. Α2;1?Ρ >Β2 ≅2? Χ2?1.12?.; . =.?Α6? 12 .Η?:.06<;2≅ =<12:<≅ 0<;≅Α?Β6? <Α?.≅ .Η?:.06<;2≅.
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9.≅ .Η?:.06<;2≅ >Β2 0<:=<;2; 9.≅ .Η?:.06<;2≅ ;Β2Χ.≅, =<1?2:<≅ 121Β06? 29 Χ.9<? 12 Χ2?1.1 12 9. .Η?:.06Ω; >Β2 ≅2 0<;≅Α?ΒΦ..
!<≅ 0<;20Α6Χ<≅ 9Ω460<≅, Α62;2; Β;. ;<Α.06Ω; 2≅=206.9 Φ ≅Β ≅2;Α61< 2; :.Α2:ΡΑ60.≅ 2≅ =?206≅<.
C.1. =?<=<≅606Ω; Α62;2 Β;. 3<?:. 9Ω460. . 9. 0Β.9 ≅2 92 1. Β; ;<:/?2. (2 16≅Α6;4Β2; 1<≅ Α6=<≅ 12 =?<=<≅606<;2≅: 5−03/)5Φ ∋2037)56%5. ∗;. =?<=<≅606Ω; ≅2 12;<:6;. ≅6:=92 0Β.;1< 299. ;< 6;Α2?Χ62;2 ;6;4Β;. 0<;20Α6Χ. 9Ω460. < ΑΤ?:6;< 12 2;9.02 (Φ, <, ;<, ≅6,... 2;Α<;02≅..., ≅6 Φ ≅Ω9< ≅6). (6 ≅2 7Β;Α.; Β;. < Χ.?6.≅ =?<=<≅606<;2≅ ≅6:=92≅ 0<; Β; ΑΤ?:6;< 12 2;9.02, ≅2 3<?:. Β;. =?<=<≅606Ω; 0<:=Β2≅Α.. !<≅ ΑΤ?:6;<≅ 12 2;9.02, ΛΦΜ, Λ<Μ, Λ≅6...2;Α<;02≅Μ, Λ≅6 Φ ≅Ω9< ≅6Μ; ≅2 Β≅.; =.?. 964.? 1<≅ =?<=<≅606<;2≅, 2; 0.:/6< 29 ΑΤ?:6;< 12 2;9.02 Λ;<Μ ≅2 .4?24. . Β;. ≅<9. =?<=<≅606Ω;.
!. 3<?:. 12 9.≅ =?<=<≅606<;2≅ 0<:=Β2≅Α.≅ 12=2;12 129 ΑΤ?:6;< 12 2;9.02 ΒΑ696Γ.1<, Φ ;< 129 0<;Α2;61< 12 9. =?<=<≅606Ω; < =?<=<≅606<;2≅ ≅6:=92≅. E≅ 1206? ≅6 2; Β;. =?<=<≅606Ω; 0<:=Β2≅Α. ≅2 ≅Β≅Α6ΑΒΦ2; 9.≅ =?<=<≅606<;2≅ ≅6:=92≅ =<? <Α?.≅ =?<=<≅606<;2≅ ≅6:=92≅ 0Β.92≅>Β62?., 9. 3<?:. 12 9. =?<=<≅606Ω; 0<:=Β2≅Α. ≅2 0<;≅2?Χ..
O&5)48%∋−Β1: G2;2?.9:2;Α2 =.?. ?2=?2≅2;Α.? 9.≅ =?<=<≅606<;2≅ ΒΑ696Γ.:<≅ 92Α?.≅ 9.Α6-;.≅ :.ΦΞ≅0Β9.≅ < :6;Ξ≅0Β9.≅ 0<:< +; ,; −; :::
)2;62;1< 0<:< /.≅2 9.≅ .Η?:.06<;2≅: P: ΛE∀ ∗ab∀e(% de e)∗e )a∀6∃ e) ,e(deΜ, Q: ΛE∀ ∗ab∀e(%
de∀ )a∀6∃ 315 e) b∀a∃c%Μ, =<12:<≅ 0<;≅Α?Β6? ;Β2Χ.≅ .Η?:.06<;2≅, =<? 272:=9<: P Φ Q: ΛE∀
∗ab∀e(% de e)∗e )a∀6∃ e) ,e(de . e∀ ∗ab∀e(% de∀ )a∀6∃ 315 e) b∀a∃c%Μ,P <Q: ΛE∀ ∗ab∀e(% de e)∗e )a∀6∃ e) ,e(de % e∀ ∗ab∀e(% de∀ )a∀6∃ 315 e) b∀a∃c%1.
∀%&/%5 () 8)4(%( %.?. 2Χ6Α.? .:/64Ψ21.12≅, 12Η;6:<≅ 29 Β≅< 12 9<≅ ≅Υ:/<9<≅ :216.;Α2 Α./9.≅ 12 Χ2?1.1.
E≅Α.≅ Α./9.≅ =Β212; 0<;≅Α?Β6?≅2 5.062;1< Β;. 6;Α2?=?2Α.06Ω; 12 9<≅ 9Ω460<≅,;_;^;=); ()
C21.71∋−Β1 (^) (C<??2≅=<;12 .9 ΜΦΜ 129 92;4Β.72 0<:Ξ;). (2.; P Φ Q .Η?:.06<;2≅. !.
.Η?:.06Ω; P^Q≅2 922 ΜP Φ QΜ 2≅ 6;ΑΒ6Α6Χ.:2;Α2 Χ2?1.12?. ≅6 .:/.≅ ≅<; Χ2?1.12?.≅ Φ 3.9≅. ≅6 .94Β;. 12 299.≅ 2≅ 3.9≅., =2?< ≅Β 12Η;606Ω; =?206≅. ≅2 0<;≅64;. 2; 9. ≅64Β62;Α2 Α./9., >Β2 99.:.:<≅ Α./9. 12 Χ2?1.1.
P Q P ^Q
V V V
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F V F
F F F
N26%: E; 29 92;4Β.72 0<:Ξ; 9. =.9./?. ΜΦΜ =<1?Ρ Α2;2? <Α?<≅ ≅64;6Η0.1<≅ (=2?<, Α.:/6Τ;, .Ξ;), ≅6; 2:/.?4< =.?. ;<≅<Α?<≅ 29 ≅64;6Η0.1< 2≅ 29 >Β2 ;<≅ 1. 9. Α./9..
D−5:71∋−Β1 (_) (C<??2≅=<;12 .9 Μ<Μ 129 92;4Β.72 0<:Ξ;). !.≅ .Η?:.06<;2≅ P _Q ≅2 922
ΜP Ω QΜ, 6;ΑΒ6Α6Χ.:2;Α2 P _Q 2≅ Χ2?1.12?< ≅6 0Β.9>Β62?. 12 9.≅ 1<≅ .Η?:.06<;2≅ 9< 2≅ < ≅6 .:/.≅ 9< ≅<;.
P Q P _Q
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F V V
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N26%: E≅Α2 2; Β; Μ<Μ 6;09Β≅6Χ< Φ ;< 2Ε09Β≅6Χ<. E; 29 92;4Β.72 0<9<>Β6.9 :Β05.≅ Χ202≅ ;< ≅2 =2?:6Α2 >Β2 .:/.≅ ≅2.; Χ2?1.12?.≅.
D2≅=ΒΤ≅ 129 .9:Β2?Γ< 0<:< =<≅Α?2 < :2 9.Χ< 9<≅ 162;Α2≅. E; 9. .Η?:.06Ω; .;Α2?6<? 1.1. 2; 92;4Β.72 0<:Ξ; Β;< 2;Α62;12 >Β2 ;< 5.?Ρ 9.≅ 1<≅ 0<≅.≅ 12≅=ΒΤ≅ 12 .9:Β2?Γ<. A>ΒΥ 29 Μ<Μ 2≅ 2Ε09Β≅6Χ<, =2?< 2; 29 92;4Β.72 :.Α2:ΡΑ60< 29 Μ<Μ >Β2 ≅2 Β≅. 2≅ 29 6;09Β≅6Χ<.
N)+%∋−Β1 () (C<??2≅=<;12 .9 Μ;<Μ 129 92;4Β.72 0<:Ξ;). !. .Η?:.06Ω; P >Β2 ≅2 922
";<P", 6;ΑΒ6Α6Χ.:2;Α2 P 2≅ 3.9≅< 0Β.;1<P 2≅ Χ2?1.12?< ΦP 2≅ Χ2?.12?< 0Β.;1< P ;<
9< 2≅. !. 12Η;606Ω; =?206≅. 12 9. ;24.06Ω; 2≅:
P P
V F
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P : E9 Α./92?< 12 2≅Α2 ≅.9Ω; ;< 2≅ Χ2?12.
AΒ;>Β2 2≅ ≅6:=92, ;< 12/2 0<;3Β;16?≅2 P 0<; 9< 0<;Α?.?6< 12 P:
!. ;24.06Ω; 12 "J+a∃ e) (ic%"; ;< 2≅ "J+a∃ e) &%b(e"
C21(−∋−21%/ ( !) (C<??2≅=<;12 .9 Μ(6,...,2;Α<;02≅...Μ 129 92;4Β.72 0<:Ξ;). !. .Η?:.06Ω;
P ! Q ≅2 922 Μ(6 P 2;Α<;02≅ QΜ, 6;ΑΒ6Α6Χ.:2;Α2 2≅ Χ2?1.12?. ≅6 ;Β;0. <0Β??2 >Β2 P ≅2.
Χ2?1.12?. Φ >Β2 Q ≅2. 3.9≅< .9 :6≅:< Α62:=<. !. 12Η;606Ω; =?206≅. 2≅:
P Q P !Q
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!.≅ 1<≅ =?6:2?.≅ 9Υ;2.≅ ≅<; Μ0?26/92≅Μ, 9.≅ 1<≅ Ξ9Α6:.≅ ;<≅ 0Β2≅Α.; :Ρ≅ Α?./.7<. )?.Α2:<≅ 12 2;Α2;12?9.≅ 0<; 29 ≅64Β62;Α2 272:=9<.
ΜSi J%(ge )e ∗%#a ∀a) )%&a), e∃∗%∃ce) .% ∀e c%#&(% +∃ he∀ad%1. ΠCΒΡ9 ≅2?Υ. 29 Ξ;60< 0.≅< 2; 29 >Β2 J<?42 ?209.:.?Υ.?. E≅ 09.?< >Β2 ≅6 J<?42 ≅2 Α<:. 9.≅ ≅<=.≅ Φ Φ< 92 0<:=?< 29 529.1<, 2;Α<;02≅ 9. .Η?:.06Ω; 0<;1606<;.9 ≅2 Χ2?6Η0.; ).:/6Τ; 2≅ 09.?< >Β2 ≅6 J<?42 ≅2 Α<:. 9.≅ ≅<=.≅ Φ Φ< ;< 92 0<:=?< 29 529.1<, 2;Α<;02≅ 9. .Η?:.06Ω; 0<;1606<;.9 ;< ≅2 Χ2?6Η0.; .5<?., ≅6 J<?42 ;< ≅2 Α<:. 9.≅ ≅<=.≅ Φ Φ< 92 0<:=?< 29 529.1<, 2;Α<;02≅ 9. .Η?:.06Ω; 0<;1606<;.9 ≅2 Χ2?6Η0.. %<? Ξ9Α6:<, ≅2 0Β:=92 >Β2 ≅6 J<?42 ;< ≅2 Α<:. 9.≅ ≅<=.≅ Φ Φ< ;< 92 0<:=?< 29 529.1<, 9. .Η?:.06Ω; 0<;1606<;.9 ≅2 Χ2?6Η0..
P ! Q ≅2 =Β212 2≅0?6/6? Q P: D<;12 P 2≅ 29 .;Α20212;Α2 Φ Q 2≅ 29 0<;≅20Β2;Α2. A≅Υ =Β2≅, 9<≅ 1<≅ Ξ9Α6:<≅ ?2;49<;2≅ 12 9. Α./9. 9<≅ 6;Α2?=?2Α.:<≅ .≅Υ: (6 29 .;Α20212;Α2 2≅ 3.9≅<, 0Β.9>Β62? 0<≅. =Β212 <0Β??6? 0<; 29 0<;≅20Β2;Α2.
P ! Q ≅2 922 Μ≅6 P; QΜ; ΜQ ≅6 PΜ; ΜP ≅Ω9< ≅6 QΜ; ΜQ ≅62:=?2 >Β2 PΜ; Μ≅Β=<;62;1< P, 2;Α<;02≅ QΜ; ΜQ 1.1< >Β2 PΜ; ΜP 2≅ ≅ΒΗ062;Α2 =.?. QΜ Φ ΜQ 2≅ ;202≅.?6< =.?.PΜ.
2. += 2( =.?. .94Ξ;( 2Z, ≅6+ 2≅ =.?.
3. + 2≅ Β; ;Ξ:2?< =.?. ≅Ω9< ≅6 += 2( =.?. .94Ξ; (2Z. 4. += 2( =.?. (2Z ≅62:=?2 >Β2 + ≅2. =.?.
5. (Β=<;62;1< >Β2 + ≅2. =.? 2;Α<;02≅+= 2( =.?. .94Ξ; ( 2Z.
6. + 2≅ =.? 2≅ ≅ΒΗ062;Α2 =.?. >Β2 += 2( =.?. .94Ξ; (2Z. 7. += 2( =.?. .94Ξ;( 2Z 2≅ ;202≅.?6< =.?. >Β2+ ≅2. =.?.
B−∋21(−∋−21%/ ( !) Λ(6 Φ ≅Ω9< ≅6Μ. !. .Η?:.06Ω; P !Q 6;ΑΒ6Α6Χ.:2;Α2 ;<≅ 1602 >Β2 2≅ Χ2?1.12?. ≅62:=?2 >Β2 P Φ Q ≅2.; .:/.≅ Χ2?1.12?.≅ < .:/.≅ 3.9≅.≅, =2?< >Β2 2≅ 3.9≅< 2; 0.≅< 0<;Α?.?6<.
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F F V
"Y% e)∗+dia(4 f+∃da#e∃∗%) h%. )i . )6∀% )i ∗7 ∀% hace) ∗a#bi4∃".
E≅Α< ≅2 Χ2?6Η0. ≅6 .:/<≅ 2≅ΑΒ16.:<≅ < .:/<≅ ;< 9< 5.02:<≅, =2?< 09.?.:2;Α2 ≅6 Φ< 9< 5.4< Φ ΑΒ ;< 9< 5.02≅ ;< ≅2 Χ2?6Η0. (< Χ602Χ2?≅.). E≅ 1206?, ;< =Β212 ≅2? 29 0.≅< >Β2 Β;< 2≅ΑΒ162 Φ 29 <Α?< ;<.
∃Α?.≅ 3<?:.≅ 12 922? P ! Q; Q ! P; P ≅6 Φ ≅Ω9< ≅6 Q, P ≅6 Φ ≅<9.:2;Α2 ≅6 Q, P 2≅ ;202≅.?6< Φ ≅ΒΗ062;Α2 =.?. Q. ).:/6Τ; =<12:<≅ 2≅0?6/6? . P ! Q =<? Q ! P; . Χ202≅
./?2Χ6.:<≅ Μ≅6 Φ ≅Ω9< ≅6Μ =<? Μ≅66Μ.
≅2 0.90Β9. 0<:< ≅64Β2:
P Q P _Q P ^Q Q^P (P _Q)^Q^P
V V V V F F
V F V F V V
F V V F V V
F F F V F F
E≅Α< 2≅,
P Q P YQ
V V F
V F V
F V V
F F F
O&5)48%∋−Β1
(6P ΦQ≅<; =?<=<≅606<;2≅, 2;Α<;02≅PYQ2≅ Β;. =?<=<≅606Ω; >Β2 2≅ Χ2?1.12?. =?206≅.:2;Α2 0Β.;1< 9<≅ Χ.9<?2≅ 12 Χ2?1.1 12 P Φ Q;< 0<6;0612;. E; <Α?.≅ =.9./?.≅, P YQ 2≅ Χ2?1.12?.
≅6 ≅2 Α62;2 >Β2 ≅Ω9< P 2≅ Χ2?1.12?, < ≅2 Α62;2 >Β2 ≅Ω9< Q 2≅ Χ2?.12?., =2?< ;< 0Β.;1< .:/.≅
≅<; Χ2?.12?.≅ ;6 0Β.;1< .:/.≅ ≅<; 3.9≅.≅. (I9Β≅Α?.06Ω;)
1. )?Ρ6;4.;9< Χ6Χ< < (Α?Ρ6;4.;9<) :Β2?Α< 2≅ Β;. 6;≅Α.;06. 12 9. 16≅ΦΒ;06Ω; 2Ε09ΒΦ2;Α2. 2. (6>2)Y(6<2) 2≅ Β;. 272:=9< :Ρ≅ 3<?:.9.
O&5)48%∋−Β1
CΒ.;1< ≅2 Α?./.7. 0<; =?<=<≅606<;2≅, 2≅ 6;16≅=2;≅./92 29 /Β2; Β≅< 12 9<≅ =.?Τ;Α2≅6≅; ≅Β 12≅-0Β61< =?<Χ<0. ;Β:2?<≅<≅ 2??<?2≅.
E9 =.=29 12 9<≅ =.?Τ;Α2≅6≅ 2≅ ≅6:69.? .9 12 9. =Β;ΑΒ.06Ω; 2; ;Β2≅Α?. 4?.:ΡΑ60.; ≅2=.?. Β;61.12≅ :Ρ≅ =2>Β2ς.≅ 12;Α?< 129 16≅0Β?≅<.
(Β 6:=<?Α.;06. ?.160. 2; >Β2 12/2:<≅ =?<0Β?.? >Β2 9< >Β2 2≅0?6/.:<≅ 2; ∀.Α2:ΡΑ60.≅ ;< 2≅ΑΤ ≅Β72Α< . 6;Α2?=?2Α.06<;2≅ 16≅Α6;Α.≅, 2≅ 1206?, >Β2 0.?2Γ0. 12 .:/64Ψ21.1.
)<:2 2; 0Β2;Α. >Β2 Β; 0.:/6< 2; 9. =Β;ΑΒ.06Ω; =Β212 :<16Η0.? 0<:=92Α.:2;Α2 29 ≅2;Α61< 12 9. 3?.≅2.
E9 Β≅< 12 =.?Τ;Α2≅6≅ 2; =?<=<≅606<;2≅ Α62;2 .;Ρ9<4. ΒΑ6961.1 Φ ≅6:69.?2≅ 0<;Χ2;06<;2≅ >Β2 29 Β≅< 12 =.?Τ;Α2≅6≅ 2; 2Ε=?2≅6<;2≅ .942/?.60.≅. ).:/6Τ; 2; 29 Ρ942/?. 292:2;Α.9 =Β212 0.:/6.? 29 ≅64;6Η0.1< 12 9. 2Ε=?2≅6Ω; ≅24Ξ; 9<≅ Μ≅2=.?.1<?2≅Μ >Β2 ≅2 2:=92..
+2.:<≅ .94Β;<≅ ≅6ΑΒ.06<;2≅:
1. C<;≅612?2 9. 0<;<061. Φ :.9 5205. =?24Β;Α. ΠCΒΡ9 2≅ 9. :6Α.1 12 1<≅?. C<:< ≅2 ≅./2, 9. ?2≅=Β2≅Α. 12=2;12 12 ≅6 Β≅Α21 2;Α62;12 9. =?24Β;Α. 0<:<
1 2
2
+ 2; Ω /62;
1
2 (2 + 2):
2. #<Α2 ≅6; 2:/.?4< >Β2 0Β.;1< ≅2 2≅0?6/2 ab+c Α<1< 29 :Β;1< 2;Α62;12 (ab) +c Φ ;<
a(b+c):
E; <Α?.≅ =.9./?.≅, ≅6 Β≅Α21 >Β62?2 2≅0?6/6? (ab) +c; =Β212 2≅0?6/6? ab+ c; =2?< ≅6 >Β62?2
2≅0?6/6?9< Α.9 0Β.9.
%.?. ?232?6?≅2 . 2≅Α. ≅6ΑΒ.06Ω; 0<;Χ2;06<;.9, ≅2 ≅Β292 1206? >Β2 Μ9. ≅Β:. =?2Χ.9202 ≅</?2 9. :Β9Α6=960.06Ω;Μ, Ω /62; >Β2 Μ29 =?<1Β0Α< ≅2 5.02 .;Α2≅ >Β2 9. ≅Β:.Μ.
E≅Α.≅ 2Ε=?2≅6<;2≅ 2; 2≅=.ς<9 ;< ≅<; 2Ε0292;Α2≅, =2?< ;< Α?.2; =?</92:. ≅6 ≅2 9.≅ Β≅. 0<??20-Α.:2;Α2.
E; 0Β.9>Β62? 0.≅<, Β≅Α21 =Β212 2≅0?6/6? 2 + 35 Φ Α<1<≅ 2;Α2;12?Ρ; 17(Φ ;< 25).
3. A5<?. /62;, ≅6 Β≅Α21 >Β62?2 2≅0?6/6? 29 ;Ξ:2?< a(bc) =Β212 2≅0?6/6? abc; =2?< =Β212
2≅0?6/6? Α.:/6Τ; abc =.?. 2Ε=?2≅.?(ab)c:
E≅Α< ≅2 12/2 . 9. 92Φ 12 9. .≅<06.Α6Χ61.1 2; 9<≅ ;Ξ:2?<≅, >Β2 1602 >Β2 ≅6 Α62;2 a(bc) = (ab)c
Φ 2;Α<;02≅, 9. 2Ε=?2≅6Ω; abc =Β212 ≅64;6Η0.? 0Β.9>Β62?. 12 9.≅ 1<≅. E1 )/ ?/+)&4% () 342325−∋−21)5
CΒ.;1< ≅2 Α?./.7. 0<; =?<=<≅606<;2≅, 9. ≅6ΑΒ.06Ω; 2≅ .;Ρ9<4. . 9. 92Φ 12≅0?6Α..
1. (A≅<06.Α6Χ61.1): !.≅ =?<=621.12≅ 12 .≅<06.Α6Χ61.1 12 9. 0<;7Β;06Ω; Φ 12 9. 16≅ΦΒ;06Ω; 6;160.; >Β2,
(P ^Q)^R () P ^(Q^R)
Φ
E≅Α< =2?:6Α6?Ρ 2≅0?6/6? ≅6; .:/64Ψ21.1
P ^Q^R
Φ
P _Q_R
A94< .;Ρ9<4< <0Β??2 0<; 9. 16≅ΦΒ;06Ω; 2Ε09ΒΦ2;Α2.
2. (ΚD6≅Α?6/ΒΑ6Χ61.1Κ): C<;Α?.?6< . 9. .≅<06.Α6Χ61.1, ;< ≅2 Α62;2 >Β2;
(P ^Q)_R () P ^(Q_R)
0<:< Α.:=<0< ≅2 Α62;2
(P _Q)^R () P _(Q^R)
(!< .;Α2?6<? ≅2 =Β212 0<:=?</.?, =<? 72:=9<, 5.062;1< 9. Α./9. 12 Χ2?1.1 ?2≅=20Α6Χ.). E≅Α< </964. . 2≅0?6/6? 0<; 9<≅ ?2≅=20Α6Χ<≅ =.?Τ;Α2≅6≅: Φ. ≅2. 2Ε.0Α.:2;Α2 (P ^Q)_R ≅6 2≅ >Β2 =62;≅. 2; 2≅. 2Ε=?2≅6Ω;, < /62; =?206≅.:2;Α2 P ^(Q_−) ≅6 2≅< 2≅ 9< >Β2 >Β62?2 2≅0?6/6?.
3. (#< .≅<06.Α6Χ61.1): D2 .;Ρ9<4. :.;2?., =<12:<≅ Χ2? >Β2
(P =)Q) =) R ;< 2≅ 2>Β6Χ.92;Α2 . P =)(Q=)R)
Φ >Β2, P () (Q () R) ;< 2≅ 2>Β6Χ.92;Α2 . P () (Q () R);
Φ .≅Υ, 2; 2≅Α<≅ 0.≅<≅, 2≅ 6;16≅=2;≅./92 2≅0?6/6? 9<≅ =.?Τ;Α2≅6≅.
4. D2 .0Β2?1< . =?<=621.12≅ >Β2 ≅2 Χ2?Ρ :Ρ≅ .129.;Α2 Φ =.?. ≅6:=96Η0.? 9. 2≅0?6ΑΒ?., ≅2 0<;Χ62;2 >Β2 ∀a i#&∀icaci6∃ . ∀a e∋+i,a∀e∃cia &(e,a∀ece∃ )%b(e ∀a c%∃ +∃ci6∃ . ∀a di).+∃ci6∃.
E≅Α< ≅64;6Η0., =<? 72:=9<, >Β2 9. 2Ε=?2≅6Ω; P ^Q =) R ≅64;6Η0. (P ^Q) =) R =2?<
P ^Q=)R ;< ≅64;6Η0. P ^(Q=)R):
I;≅6≅Α6:<≅ 2; >Β2 ≅2 Α?.Α. .>ΒΥ ≅Ω9< 12 Β;. 0<;Χ2;06Ω; =.?. ≅6:=96Η0.? 9. 2≅0?6ΑΒ?. (;< 5.Φ 2; 2≅Α< .94< ;202≅.?6< ≅6;< ≅6:=92:2;Α2 0<;Χ2;62;06.).
5. E≅ 0<;Χ2;62;Α2 Α.:/6Τ; 2; 2≅0?6/6?(P) 2; 9Β4.? 12 P
1. (2 =Β212 2≅0?6/6?, ≅6; .:/64Ψ21.1 Φ =<? =?<=621.12≅ 9< ≅64Β62;Α2:
P ^Q^R; P _Q_R; P YQYR:
2. (2 =Β212 2≅0?6/6?, ≅6; .:/64Ψ21.1 Φ =<? 0<;Χ2;06<;2≅,
P ^Q=)R; P _Q=)R; 2Α0.
3. #< ≅2 12/2 2≅0?6/6?, =Β2≅ ;< ≅<; =?<=<≅606<;2≅,
P ^Q_R; P _Q^R; P =)Q=)R; P () Q () R; P =)Q () R;
(;< ≅2 Α62;2; =?<=621.12≅ ;6 0<;Χ2;6<≅ >Β2 =2?:6Α.; ≅6>Β62?. 2≅0?6/6?9.≅). ∃/≅2?Χ2 .9 =.≅.? >Β2 9. 3?.≅2 T%#% e∀ b+) . c%#% ch%c%∀a∗e % beb% ag+a.
)62;2 1<≅ 6;Α2?=2Α?.06<;2≅ 16≅Α6;Α.≅ Ν≅24Ξ; 1Ω;12 ≅2 =<;4. 9. ≅2=.?.06Ω; (9. 0<:., 29 =.?Τ;Α2≅6≅)Ν Φ =<? Α.;Α< ;< =<12:<≅ .02=Α.?9..
B62; 2;Α2;161<, 9<≅ ≅64Β62;Α2≅ 0Β.1?<≅ 0<;Α62;2; Α<1. 9. 6;3<?:.06Ω; ?292Χ.;Α2 12 2≅Α. ≅2006Ω;:
P P
V F
F V
;
P Q P _Q P ^Q P =)Q P () Q P YQ
V V V V V V F
V F V F F F V
F V V F V F V
F F F F V V F
∀%762/2+Α%5 (I;3<?:.9:2;Α2): ∋2≅=20Α< 12 9<≅ 99.:.1<≅ Χ.9<?2≅ 12 Χ2?1.1, ≅2 1602 >Β2 Β;. =?<=<≅606Ω; 2≅ Β;. Α.ΒΑ<9<4Υ. ≅6 2≅ ≅62:=?2 Χ2?1.12?., Β; ./≅Β?1< < 0<;Α?.16006Ω; ≅6 2≅ ≅62:=?2 3.9≅. < /62; Β;. 0<;Α6;42;06. (. Χ202≅ Χ2?1.12?., . Χ202≅ 3.9≅.).
(A;Β;06.:<≅ =?<Χ6≅<?6.:2;Α2 >Β2) ≅6P; Q≅<; =?<=<≅606<;2≅ 0Β.92≅>Β62?., 2;Α<;02≅P _P 2≅ Β;. Α.ΒΑ<9<4Υ., P ^P 2≅ Β; ./≅Β?1< Φ P _Q 2≅ Β;. 0<;Α6;42;06. (. :2;<≅ >Β2 + ≅2. Β;.
Α.ΒΑ<9<4Υ., < >Β2 Q ≅2. Β;. Α.ΒΑ<9<4Υ., < /62; >Β2 P Φ Q ≅2.; ./≅Β?1<≅).
∀%762/2+Α% −03246%16)5 A 0<;Α6;Β.06Ω; =?</.?2:<≅ Β;. 0<92006Ω; 12 Α.ΒΑ<9<4Υ.≅ 6;Α2?2-≅.;Α2≅, .94Β;.≅ 12 299.≅ 0<; ;<:/?2 =?<=6<.
%<? ≅Β=Β2≅Α<, ≅24Ξ; 9. 12Η;606Ω;, ≅6_Φ_0≅<; Α.ΒΑ<9<4Υ., Α.:/6Τ; 9<≅ ≅<;_^_0 ;___0
;_ ()
_0, _=) _0; 2Α0.
#< 2≅ΑΡ 12:Ρ≅ .1Χ2?Α6? >Β2 9. =?<=<≅606Ω;_ () _0 >Β2 .0./.:<≅ 12 2≅0?6/6? ≅64;6Η0. >Β2
Α<1.≅ 9.≅ Α.ΒΑ<9<4Υ.≅ ≅<; 2>Β6Χ.92;Α2≅ 2;Α?2 ≅6.
I?2:<≅ 6;160.;1<, 0.1. Χ2Γ 9. 6:=<?Α.;06. ?29.Α6Χ. 12 9.≅ 16Χ2?≅.≅ Α.ΒΑ<9<4Υ.≅, 0ΒΡ92≅ 5.Φ >Β2 Α2;2? ≅62:=?2 =?2≅2;Α2≅ Φ 0ΒΡ92≅ ≅2 1209.?.; =.?. ≅2? Μ<9Χ61.1.≅Μ 12 6;:216.Α< Ν.94Β;.≅ ≅<; /.≅Α.;Α2 3Ρ0692≅ 12 ?2Α2;2?Ν:
H.Φ Α?2≅ :.;2?.≅ 12 12 =?</.? Α.ΒΑ<9<4Υ.≅:
1. ∗≅.? Α./9.≅ 12 Χ2?1.1. E99< ≅2 5.02 12 :<1< .;Ρ9<4< . 0<:< 52:<≅ :<≅Α?.1< 2; 9. ≅2006Ω; .;Α2?6<?, 0Β61.;1< 12 2≅0?6/6? <?12;.1.:2;Α2 Α<1.≅ 9.≅ 0<:/6;.06<;2≅ 12 Χ.9<?2≅ 12 Χ2?1.1 =<≅6/92≅ 2;Α?2 9.≅ =?<=<≅606<;2≅ >Β2 6;Α2?Χ62;2; (Α<:2 ;<Α. 12 9. 16≅=<≅606Ω; >Β2 ΒΑ696Γ.?2:<≅).
2. H.02? 12?6Χ.06Ω; < Β≅.? Ρ942/?. 12 =?<=<≅606<;2≅, 2≅ 1206?, =?<0212? .9 :<1< .942/?.60<. E≅Α< ≅64;6Η0. >Β2, . :2161. >Β2 ≅2 Χ. =?</.;1< 12Α2?:6;.1<≅ ?2≅Β9Α.1<≅, ≅2 9<≅ =Β212 6? Β≅.;1< =.?. ≅6:=96Η0.? < 2≅Α./9202? <Α?.≅ =?<=621.12≅.
3. ∗Α696Γ.? 29 :ΤΑ<1< 6;16?20Α<, 2; =.?Α60Β9.? 9. 99.:.1. ?21Β006Ω; .9 ./≅Β?1<.
A>ΒΥ Β≅.?2:<≅ =?6:2?< Α./9.≅ 12 Χ2?1.1. ∗;. Χ2Γ =?</.1.≅ 9.≅ Α.ΒΑ<9<4Υ.≅ 3Β;1.:2;Α.92≅, =<12:<≅ 6;Α2;Α.? 5.02? 12?6Χ.06Ω;. ∀Ρ≅ .129.;Α2 Χ<9Χ2?2:<≅ 2Ε=?2≅.:2;Α2 ≅</?2 9<≅ :ΤΑ<1<≅ 12 12:<≅Α?.06Ω;.
%?</.?2:<≅ ≅Ω9< .94Β;.≅ Α.ΒΑ<9<4Υ.≅, Φ 1272:<≅ . Β≅Α21 9. <=<?ΑΒ;61.1 12 12:<≅Α?.? 9.≅ ?2≅Α.;Α2≅ Φ. ≅2. 6:6Α.;1< 9.≅ >Β2 .>ΒΥ 5.02:<≅ < /62; 6;Χ2;Α.;1< <Α?.≅. E; 0Β.9>Β62? 0.≅<, .≅24Ξ?2≅2 =?6:2?< 12 >Β2 =Β212 5.02? 9. 12:<≅Α?.06Ω; 12 0.1. Α.ΒΑ<9<4Υ. :216.;Α2 Α./9.≅ 12 Χ2?1.1; 9Β24< =Β212 2≅ΑΒ16.? 9. 12≅0?6=06Ω; 12 9<≅ <Α?<≅ :ΤΑ<1<≅.
C<:< ≅2 Χ2?Ρ, 9.≅ 12:<≅Α?.06<;2≅ 2; 9.≅ >Β2 ≅2 Β≅. Α./9.≅ 12 Χ2?1.1 ≅<; 6;12=2;162;Α2≅ Β;.≅ 12 <Α?.≅. H2:<≅ <?12;.1<, ≅6; 2:/.?4<, 9. 96≅Α. 12 Α.ΒΑ<9<4Υ.≅ =.?. >Β2 12≅=ΒΤ≅ =<1.:<≅ Β≅.? Β;.≅ =.?. 12:<≅Α?.? <Α?.≅ .9 :<1< .942/?.60<.
E; 0Β.9>Β62? 0.≅<, 9. 612. ;< 2≅ .=?2;12? Β;. 96≅Α. 12 :2:<?6. ≅6;< 0<;≅612?.? 0<; 09.?61.1 0.1. ≅6ΑΒ.06Ω;. C<:=?</.?Ρ Β≅Α21 >Β2 Χ.?6.≅ 12 9.≅ 96≅Α.≅ 12 9.≅ Α.ΒΑ<9<4Υ.≅ ≅<; 3Ρ0692≅ 12 ?2Α2;2?.
(6 _;_0 ≅<; Α.ΒΑ<9<4Υ.≅ Φz
;z0 ≅<; ./≅Β?1<≅, 2;Α<;02≅:
1. _ () _0
2. z () z0
4. _ () z
%<? 272:=9<,
_ _0 _ () _0
V V V ;
_ z _ _ () z
V F F F ; /c:
(2 Α?.Α. 12 Β;. =?<=<≅606Ω; /.≅Α.;Α2 ≅6:=92: )<1<≅ 9<≅ ./≅Β?1<≅ 2>Β6Χ.92;Α2≅, Α<1.≅ 9.≅ Α.ΒΑ<9<4Υ.≅ ≅<; 2>Β6Χ.92;Α2≅, 2Α0.
(6 _;_0 ≅<; Α.ΒΑ<9<4Υ.≅ Φz
;z0 ≅<; ./≅Β?1<≅ ΦP 2≅ Β;. =?<=<≅606Ω; 0Β.9>Β62?., 2;Α<;02≅:
1. P =) _
2. z=)P
3. P ^z () _
4. P _ _ () _
5. P _z () P
6. P ^ _ () P
%<? 272:=9<,
P _ P =) _
V V V
F V V
E≅Α. 2≅ Β;. =?<=<≅606Ω; /.≅Α.;Α2 ΞΑ69 2; 9<≅ 0Ρ90Β9<≅, =2?< :ΒΦ 3.0Υ9 12 ?20<?1.? < ?2-6;Χ2;Α.?. A5<?. >Β2 52:<≅ 2≅?./92061< 2≅Α<≅ =?6:2?<≅ 1<≅ Α2<?2:.≅, 2≅0?6/6?2:< (0<:< 0.≅6 Α<1< 29 :Β;1<) V 2; 9Β4.? 12 _ Φ F 2; 9Β4.? 12 z: AΞ; 0Β.;1< 2; ?2.961.1 _;z ≅<; =?<=621.12≅
Φ V; F Χ.9<?2≅ 12 Χ2?1.1, 2≅Α2 ./Β≅< ;< ≅2 =?2≅Α.?Ρ . 0<;3Β≅6Ω;.
(6 +2≅ Β;. =?<=<≅606Ω;, 2;Α<;02≅:
1. + () +(=?6;06=6< 12 612;Α61.1)
%<? 272:=9<
+ + +^ + (+^ +)
V F F V
F V F V
E≅Α.≅ =?<=<≅606<;2≅ ≅<; /.≅Α.;Α2 ≅2;0699.≅; ≅<; Α.:/6Τ; 9<≅ Α?2≅ =69.?2≅ >Β2 =Β≅< A?6≅ΑΩΑ292≅ 2; ≅Β !Ω460. (Χ.92≅ 1206?, 2; ≅Β≅ A;.9ΥΑ60<≅).
(6 P 2≅ Β;. =?<=<≅606Ω;, 2;Α<;02≅:
1. P () +(1Β=92Ε ;24.Α6<, 1</92 ;24.06Ω;)
2. P _P () P
3. P ^P () P
C<:< ≅2 Χ2, /.≅Α.;Α2 3Ρ069 2 6;:216.Α.. (6 ;< 92 4Β≅Α. 29 9.ΑΥ;, =Β212 1206? 1</92 ;24.06Ω;. (6 P; Q≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. P ^Q () P (≅6:=96Η0.06Ω;) 2. P =)P _Q (.1606Ω;)
(6 P; Q≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. P ^Q () Q^P (0<;:ΒΑ.Α6Χ61.1)
2. +_, () ,_+(0<;:ΒΑ.Α6Χ61.1)
%<? 272:=9<,
P Q P ^Q Q^P P ^Q () Q^P
V V V V V
V F F F V
F V F F V
F F F F V
(6 P; Q; R ≅<; =?<=<≅606<;2≅, 2;Α<;02≅: 1. (P ^Q)^R () P ^(Q^R)
!. Α./9. ≅64Β62;Α2:
P Q R P _Q Q_R (P _Q)_R P _(Q_R) (P _Q)_R () P _(Q_R)
V V V V V V V V
F V V V V V V V
V F V V V V V V
F F V F V V V V
V V F V V V V V
F V F V V V V V
V F F V F V V V
F F F F F F F V
#<Α2 .5<?., >Β2 =.?. 2≅0?6/6? <?12;.1.:2;Α2 Α<1<≅ 9<≅ =<≅6/92≅ Χ.9<?2≅ 12 Χ2?1.1 12 P; Q; R
?2≅=20Α6Χ.:2;Α2, 52:<≅ 61< (12 6Γ>Β62?1. . 12?205.) 12 Β;< 2; Β;< (V F V F V F : : :); 12 1<≅
2; 1<≅ (V V F F V V : : :) Φ 12 0Β.Α?< 2; 0Β.Α?<. E; <Α?.≅ =.9./?.≅, 2≅0?6/6:<≅ ≅Β02≅6Χ.:2;Α2
12 20 2; 20; 12 21 2; 21 Φ 12 22 2; 22: (6 5Β/62?. ≅61< Β;. 0Β.?Α. =?<=<≅606Ω;, 5./?Υ.:<≅
9924.1< 5.≅Α. 2≅0?6/6? 9<≅ Χ.9<?2≅ 12 <05< 2; <05<, 2Α0. (6 P; Q; R ≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. P ^(Q_R) () (P ^Q)_(P ^R) (16≅Α?6/ΒΑ6Χ61.1).
2. P _(Q^R) () (P _Q)^(P _R) (16≅Α?6/ΒΑ6Χ61.1).
O&5)48%∋−Β1
E≅ 6:=<?Α.;Α2 0<;≅612?.? .94Β;.≅ 0Β2≅Α6<;2≅ .02?0. 12 9.≅ 92Φ2≅ 12 16≅Α?6/ΒΑ6Χ61.1: 1. E; =?6:2? 9Β4.?, Β≅.;1< 9. 0<;:ΒΑ.Α6Χ61.1, Β;< Α62;2 >Β2,=<? 272:=9<,
(P _Q)^R () R^(P _Q) () (R^P)_(R^Q) () (P ^R)_(Q^R) ;
12 :.;2?. >Β2 9. 16≅Α?6/ΒΑ6Χ61.1 3Β;06<;. Λ=<? .:/<≅ 9.1<≅Μ.
2. A5<?. /62;, ≅6 ≅2 Α62;2 Β;. 2Ε=?2≅6Ω; 129 Α6=<(P ^Q)_(R^S);≅2 =?<0212 0<:< ≅64Β2:
(P ^Q)_(R^S) () [(P ^Q)_R]^[(P ^Q)_S]
() [(P _R)^(Q_R)]^[(P _S)^(Q_S)]
E; <Α?.≅ =.9./?.≅ Φ ≅24Ξ; ≅2 6;160Ω .;Α2≅, ≅2 Α?./.7. 12 :.2?. .;Ρ9<4. .9 0Ρ90Β9< 292:2;Α.9
(a+b) (c+d) =ac+ad+bc+bd
(>Β2 ≅2 /.≅. 2; 9.≅ =?<=621.12≅ .;Ρ9<4.≅ =.?. ;Ξ:2?<≅); 0<; 9. 1632?2;06. 12 >Β2, 2; 2≅Α2 0.≅<, Α.;Α< Λ^Μ 0<:< Λ_Μ =Β212; 7Β4.? 29 =.=29 12 9. :Β9Α6=960.06Ω;, . 0<;1606Ω; 12 >Β2 29 <Α?< ≅2. 9. ≅Β:..
3. ∋2=.?2, ≅6; 2:/.?4<, 2; >Β2 =<? 272:=9<, 2; 9. 2Ε=?2≅6Ω;,(P ^Q)_(R_S);9. ≅6ΑΒ.06Ω;
2≅ 16≅Α6;Α.:
(P ^Q)_(R_S) () [(P ^Q)_R]_S
() [(P _R)^(Q_R)]_S
() (P _R_S)^(Q_R_S)
∀)24)0% 1. (Le.e) de D0M%(ga∃)
(6 P; Q; R ≅<; =?<=<≅606<;2≅, 2;Α<;02≅: 1. (P ^Q) () P_ Q
2. (P _Q) () P^ Q
!.≅ ?249.≅ 12 0<;:ΒΑ.Α6Χ61.1, .≅<06.Α6Χ61.1, 16≅Α?6/ΒΑ6Χ61.1 Φ 12 ∀<?4.; ≅<; 6:=<?Α.;Α2≅ =.?. Α?./.7.? 2; 29 Ρ942/?. 12 =?<=<≅606<;2≅ >Β2 ≅2 2Ε.:6;. :Ρ≅ .129.;Α2; =2?< ≅<; /.≅Α.;Α2 ≅2;0699.≅ 12 ?20<?1.?.
(∗≅.:<≅ 29 ;<:/?2 92Φ2≅ 12 ∀<?4.;, ≅24Ξ; 9. Α?.1606Ω;, =2?< ≅Ω9< ≅2 Α?.Α. 12 Β; =.? 12 Α2<?2:.≅).
O&5)48%∋−Β1
!. ≅64Β2;Α2 2 6:=<?Α.;Α2 =?<=621.1 ;<≅ =2?:6Α2 .12:Ρ≅ =?2≅2;Α.?, 2; ≅Β 12:<≅Α?.06Ω;, 0Ω:< 3Β;06<;. 29 :ΤΑ<1< 12 12?6Χ.06Ω;.
(6 P; Q; R ≅<; =?<=<≅606<;2≅, 2;Α<;02≅: 1. (P =)Q) () P _Q
3. (P =)Q) () Q=)P (0<;Α?.-?206=?<061.1, 0<;Α?.=<≅606Ω;).
(2 Α62;2:
1. −. 2≅ΑΡ 2≅Α./92061., ≅2 Α?.Α. 12 9. 12Η;606Ω; 12 9. 6:=960.06Ω;. 2. (2 Α62;2 ≅Β02≅6Χ.:2;Α2
P =)Q () P _Q (=<? 12Η;606Ω; 12 9. 6:=960.06Ω;) () P ^Q (=<? Β;. !2Φ 12 ∀<?4.;)
() P ^Q (=<? 1</92 ;24.06Ω;).
3. (2 Α62;2 ≅Β02≅6Χ.:2;Α2
(P =)Q) () P _Q (=<? 12Η;606Ω; 12 9. 6:=960.06Ω;) () Q_P (=<? 0<;:ΒΑ.Α6Χ61.1)
() Q_P (=<? 1</92 ;24.06Ω;)
() Q=)P (=<? 12Η;606Ω; 12 9. 6:=960.06Ω;) (6 P; Q; R ≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. (P () Q) () [(P =)Q)^(Q=)P)]
2. (P () Q) () (Q () P)
3. (P () Q) () P () Q
4. P () Q () (P YQ)
(6 Α62;2 .94Β;. 1Β1., 5.4. 9.≅ Α./9.≅ 12 Χ2?1.1 0<??2≅=<;162;Α2≅, ≅.9Χ< =.?. 29 ;Ξ:2?<1, >Β2
2≅ 9. 12Η;606Ω; 12 2>Β6Χ.92;06.. O&5)48%∋−Β1
#<Α2 >Β2 ≅2 1209.?., Α.:/6Τ; .>ΒΥ, 0<;:ΒΑ.Α6Χ61.. (6 P; Q; R ≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. P _(P ^Q) () P (./≅<?06Ω;).
!A≅ ?249.≅ 12 ./≅<?06Ω; ≅<; :ΒΦ 6:=<?Α.;Α2≅ 2; 9. =?.0Α60.. (6 Β≅Α21 6;Α2;Α. ≅6:=96Η0.? Β;. 2Ε=?2≅6Ω; 0Β.9>Β62?. Φ ;< 9< 9<4?., =?</./92:2;Α2 5.?Υ. /62; 2; 6;Α2;Α.? Β≅.? Β;. 12 299.≅. (I;Α2;Α2 12≅.??<99.?, =<? 272:=9<, P _(P ^Q) ≅24Ξ; 9. 92Φ 12 9. 16≅Α?6/ΒΑ6Χ61.1 Φ Χ2. 9< >Β2 <0Β??2 12≅12 29 0Β.?Α< =.≅<).
(6 P; Q; R ≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. (P ^Q=)R) () [P =)(Q=)R)] (2Ε=<?Α.06Ω;)
2. (P ^Q=)R) () [(P =)R)_(Q=)R)]
3. (P _Q=)R) () [(P =)R)^(Q=)R)]
4. (P =)Q^R) () [(P =)Q)^(P =)R)]
5. (P =)Q_R) () [(P =)Q)_(P =)R)]
E≅ 6;Α2?2≅.;Α2 5.02? Α<1.≅ 2≅Α.≅ 12:<≅Α?.06<;2≅ :216.;Α2 12?6Χ.06Ω;. %<? 272:=9<
(P ^Q=)R) () P ^Q_R
() P _Q_R
() P _ Q_R
() P _(Q=)R)
() [P =)(Q=)R)]
(6 P; Q≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. (P _Q)^P=)Q(≅69<46≅:< 16≅ΦΒ;Α6Χ<)
2. [(P =)Q)^P] =)Q (:<1Β≅ =<;2;≅) 3. (P =)Q)^Q =)P (:<1Β≅ Α<992;≅)
∗≅2 12?6Χ.06Ω;. %<? 272:=9<:
(P _Q)^P=)Q () (P _Q)^P _Q
() hP _Q_Pi_Q
() P _Q_P_Q
() P _Q_(P _Q)
#<Α2 >Β2 52:<≅ 2Χ6Α.1< 0<;≅062;Α2:2;Α2 9. Α2;Α.06Ω; 12 =.≅.? 12 P _Q . P ^Q:
D2 Α<1.≅ :.;2?.≅, Α.9 Α2;Α.06Ω; ;< 2≅ 4?.Χ2 Φ ≅Ω9< ≅2 Α?.1Β06?Υ. 2; >Β2 9. 12:<≅Α?.06Ω;, 0<??20Α., ?2≅Β9Α.?. Β; =<0< :Ρ≅ 9.?4. Φ :Ρ≅ 6;<02;Α2:
(P _Q)^P=)Q () (P _Q)^P _Q
() hP _Q_Pi_Q
() P ^Q_P
() P ^Q_(P _Q)
() P _Q_(P _Q) () V
([] %.?. Β;. ?2Ι2Ε6Ω; =<≅Α2?6<?: ≅6 /62; ≅2 =62;≅., 29 Α2<?2:. 12 .??6/. 2Ε=?2≅. 9.≅ :.;2?.≅
2; >Β2 Β;< Α?.1606<;.9:2;Α2 </Α6;2;2 0<;09Β≅6<;2≅). (6 +; ,; − ≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. [(+=),)^(+=)−)] =)(+=)−) (Α?.;≅6Α6Χ61.1). 2. [(+ () ,)^(+ () −)] =)(+ () −)(Α?.;≅6Α6Χ61.1).
(6 +; ,; − ≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. (+ () ,) =)(+^− () ,^−)
2. (+ () ,) =)(+_− () ,_−)
C<:< ≅2 Χ2, ≅2 =Β212 ≅6:=96Η0.?. (6 +; ,; − ≅<; =?<=<≅606<;2≅, 2;Α<;02≅:
1. +Y, () (+ () ,)
2. (+Y,) () (+_,)^+^,
3. (+Y,) () (+^,)_(+^,)
4. +YV () +
5. +YF () +
7. [+Y(+Y−)] () [(+Y,)Y−] (.≅<06.Α6Χ61.1)
8. +^(,Y−) () [(+^,)Y(+^−)](16≅Α?6/ΒΑ6Χ61.1) 9. (+Y,) =)+_,
!. =?6:2?. .Η?:.06Ω; 2≅ 6;:216.Α. ≅24Ξ; 9. 12Η;606Ω; 12 16≅ΦΒ;06Ω; 2Ε09ΒΦ2;Α2.
(Β=<;4. >Β2 5. 12:<≅Α?.1< 9. ≅24Β;1. =?<=621.1 :216.;Α2 Β;. Α./9.. E;Α<;02≅, =.?. 9. Α2?02?., ≅2 Α62;2 ≅Β02≅6Χ.:2;Α2:
(+Y,) () (+_,)^+^, () (+_,)^(+_,)
() (+^+)_(+^,)_(,^+)_(,^,)
() F _(+^,)_(,^+)_F
() (+^,)_(,^+)
C<:< ≅2 Χ2, 2≅Α2 Α2<?2:. 6;160. 9.≅ =?<=621.12≅ :Ρ≅ 6:=<?Α.;Α2≅ 12 9. <=2?.06Ω; ΛYΜ, 2;
=.?Α60Β9.?, 9.≅ =?<=621.12≅ 2 Φ 3 =2?:6Α2; :.;27.?9. 0<; :.Φ<? 3.06961.1.
E; 0Β.9>Β62? 0.≅< 2≅Α. <=2?.06Ω; .=.?202 :2;<≅ >Β2 9<≅ <Α?<≅ 0<;20Α6Χ<≅ 2; 9. =?.0Α60. :.Α2:ΡΑ60. 0<??62;Α2.
1.3. A/+)&4% () 342325−∋−21)5
1.3.1. L% 4)+/% () 5756−67∋−Β1E≅ 2≅ΑΡ Β;. 6:=<?Α.;Α2 ?249., >Β2 52:<≅ Β≅.1< .;Α2?6<?:2;Α2 Φ >Β2 .5<?. =<;2:<≅ 2; 2Χ612;06..
CΒ.;1< 52:<≅ 2;Β;06.1< ;Β2≅Α?.≅ Α.ΒΑ<9<4Υ.≅, ≅2 2;Α62;12 0<:< ≅2 167<, >Β2 +; ,; −; ::: ≅<; =?<=<≅606<;2≅ 0Β.92≅>Β62?.; 29 5205< >Β2 9.≅ 99.:2:<≅ +; ,; − ;< 2≅ 2; ./≅<9ΒΑ< ?292Χ.;Α2.
E; <Α?.≅ =.9./?.≅, 2; Β;. Α.ΒΑ<9<4Υ. 2; >Β2 ≅2 164. +; ,; ::: Α.92≅ 92Α?.≅ 12/2; 6;Α2?=?2Α.?≅2
0<:< 2≅=.06<≅ 2; /9.;0< >Β2 ≅2 ?2992;. 0<; =?<=<≅606<;2≅.
1. a^b () b^a
2. +^, () ,^+
3. (+_−)^, () ,^(+_−)
4. [(aYb)^(/=).)] =)[(/ =).)^(aYb)]; /c:
+2.:<≅ .94Β;<≅ 272:=9<≅ :Ρ≅ ϑ0<;0?2Α<≅Κ.
%.?. ≅6:=96Η0.? 9. 2Ε=?2≅6Ω; [+^(+_(,=)−))]_ (−=)+); ≅2 =?<0212 0<:< ≅64Β2,
2;-Α2;16Τ;1<≅2 >Β2 0.1. =.≅< 2≅ Β;. 2>Β6Χ.92;06. (Β≅.?2:<≅ ./≅<?06Ω;):
[+^(+_(, =)−))]_(−=)+) [(+^+)_(+^(,_−))]_(−_+) [F _(+^,)_(+^−)]_(−_+) (+^,)_[(+^−)_(−_+)] (+^,)_[((+^−)_+)_−] (+^,)_(+_−)
((+^,)_+)_−
#<Α2 9. 6;Α2?2≅.;Α2 .=960.06Ω; 12 9. 92Φ 12 ./≅<?06Ω; 2; 9<≅ Ξ9Α6:<≅ =.≅<≅. ((6 ≅2 ≅64Β2 Α?./.-7.;1< ≅6; 299., 29 272:=9<, 2; 9Β4.? 12 ≅6:=96Η0.?≅2, 0?202?Ρ /.≅Α.;Α2, 96;2. . 96;2.).
E≅ :ΒΦ 6;Α2?2≅.;Α2 .=?2;12? . :6?.? <0.≅6<;.9:2;Α2 Β;. =?<=<≅606Ω; 12 :<1< >Β2 9. ?249. 12 ≅Β≅Α6ΑΒ06Ω; 2Χ6Α2 Β;. 0.;Α61.1 12 0Ρ90Β9<≅ ≅6; :.Φ<? =?<Χ205<.
1. D2Α2?:6;.? 29 Α6=< 12 =?<=<≅606Ω;: a) + ![(+ !−)^(, !−)]
b) [(+^,)_−] ![(+_−)^(,_−)]
c) [(+^,)^−] ![(+^,)_ −]
d) [(+_,)^ (,^ +)] ![(+^−) !,]
f) (+^,) !(+_ ,)
g) , ![+ !(+_ ,)]
h) [(+^ ,)^(+_−)]
i) f[(+_,) !,]^[(+ !−) !(, !−)]g
) [+ !(,_−)] ![(+ !,)_(+ !−)]
2. (6 + 2≅ Χ2?1.12?< (1), , 2≅3.9≅< (0) Φ − 2≅ Χ2?1.12?< (1), 12Α2?:6;.? 29 Χ.9<? 12 Χ2?1.1 12 0.1. Β;. 12 9.≅ =?<=<≅606<;2≅:
a) + ![(+ !−)^(, !−)]
b) [(+^,)_−] ![(+_−)^(,_−)]
c) [(+^,)^−] ![(+^,)_ −]
d) [(+_,)^ (,^ +)] ![(+^−) !,]
e) (+^,) ![+^(, !−)]
f) (+^,) !(+_ ,)
g) , ![+ !(+_ ,)]
h) [(+^ ,)^(+_−)]
i) f[(+_,) !,]^[(+ !−) !(, !−)]g
) [+ !(,_−)] ![(+ !,)_(+ !−)]
3. ∀216.;Α2 Β;. Α./9. 12 Χ2?1.1 12:<≅Α?.? >Β2:
(+,) ![(+^,)_(+^ ,)]
4. D2:<≅Α?.?, ΒΑ696Γ.;1< 9.≅ 92Φ2≅ 129 Ρ942/?. 12 =?<=<≅606<;2≅ >Β2: a) (+,) !(+^ ,)_(+^,)
b) (+,) ![(+^ ,)_(+^,)]
c) (+,) ![(+_,)^(+_ ,)]
5. D.1.≅ Α?2≅ =?<=<≅606<;2≅ +; ,; −; 12:<≅Α?.? ΒΑ696Γ.;1< 9.≅ 92Φ2≅ 129 Ρ942/?. 12
=?<=<≅6-06<;2≅ 9.≅ ≅64Β62;Α2≅ 2>Β6Χ.92;06.≅:
b) [(+_,)^(+_−)^(,_−)] ![(+_,)^(+_−)]
c) (+^,^−)_ (+^ ,^−)_(+^,^ −) _(+^ ,^ −) ! (+^−)_
(+^ −)
d) (+^,)^(+_,) !(+^,)_(+^ ,)
e) (+_ ,)^(,_−)^(,_ −) !(+^,)
f) (+_ ,)^(,_ −)^(+_−)^(+_ ,) !+^ ,^ −
g) [(+_,)^(+_,)] !,
h) (+^ ,)_(+^−)_(+^,) !+
i) (+^,^−)_(+_ ,_ −) !12≅ Β;. Α.ΒΑ<9<4Υ.
1.4. C7%16−<∋%(24)5
+.:<≅ . Β≅.? 9<≅ ≅Υ:/<9<≅ Λ8Μ Φ Λ9Μ. (Β Β≅< ≅2 12Α.99. :Ρ≅ ./.7<. Λ8Μ ≅2 922 =.?. Α<1<, =.?. 0.1., 0Β.9>Β62?. ≅2..
Λ9Μ ≅2 922 2Ε6≅Α2 .9 :2;<≅ Β;, < 5.Φ .9 :2;<≅ Β;, < ≅6:=92:2;Α2 2Ε6≅Α2 < 5.Φ.
∗≅.?2:<≅ 0<;7Β;Α<≅ 12 ?232?2;06.. !<≅ 0<;7Β;Α<≅ ≅2?Ρ; 2≅ΑΒ16.1<≅ 2; 29 ≅64Β62;Α2 0.=ΥΑΒ9<, =2?< 9< Ξ;60< >Β2 ;202≅6Α.:<≅ ≅./2? =<? .5<?. 2≅ >Β2 2≅ 0.?.0Α2?Υ≅Α60< 12 9<≅ 0<;7Β;Α<≅ Α2;2? 292:2;Α<≅, ≅.9Χ< 2; 29 0.≅< 129 99.:.1< 0<;7Β;Α< Χ.0Υ<.
E≅0?6/6?2:<≅ a2U =.?. 6;160.? >Β2 29 </72Α< a 2≅ Β; 292:2;Α< 129 0<;7Β;Α< U:
A;<Α.?2:<≅ .12:Ρ≅ U 6= =.?. 6;160.? >Β2 U Α62;2 .9 :2;<≅ Β; 292:2;Α<.
!.≅ 2Ε=?2≅6<;2≅:
)<1< 5<:/?2 2≅ :<?Α.9. A94Β;<≅ 5<:/?2≅ ≅<; ≅./6<≅.
=Β212; Α?.1Β06?≅2 ?2≅=20Α6Χ.:2;Α2 0<:<:
%.?. Α<1< 2, ≅6 2 2≅ 5<:/?2 2;Α<;02≅2 2≅ :<?Α.9.
EΕ6≅Α2 Β; 2, Α.9 >Β2 2 2≅ Β; 5<:/?2 Φ 22≅ ≅./6<.
∃Α?<≅ 46?<≅ ΒΑ696Γ.1<≅ =.?. 9. 2Ε=?2≅6Ω; Λ=.?. Α<1< 2Μ ≅<;:
)<1< 2;0Β.9>Β62?.2;0.1.2;>Β2 ≅2 ≅6:/<96Γ.; =<? Λ82Μ Φ ≅2 99.:.∋7%16−<∋%(24 71−8)4-5%/.
H.Φ 2; EΕ6≅Α22; Α.9 >Β2, A94Ξ; 2;A94Β;<≅ 2; >Β2 ≅2 ≅6:/<96Γ.; =<? Λ92Μ Φ ≅2 99.:. ∋7%1-6−<∋%(24 )9−56)1∋−%/.
EΕ6≅Α2; Α?2≅ 3<?:.≅ 12 0<;Χ2?Α6? Β;. 3Β;06Ω; =?<=<≅606<;.9 P 2 2; Β;. =?<=<≅606Ω;, . ≅./2?: H.062;1< 9. ≅6ΑΒ.06Ω; 12 9.≅ Χ.?6./92≅ =<? Β; ΑΤ?:6;< 2≅=20ΥΗ0<.
A;Α2=<;62;1< 9. 2Ε=?2≅6Ω; Λ=.?. Α<1< 2Μ < 0Β.;Α6Η0.1<? Β;6Χ2?≅.9.
A;Α2=<;62;1< 9. 2Ε=?2≅6Ω; Λ2Ε6≅Α2 .9 :2;<≅ Β; 2Μ < 0Β.;Α6Η0.1<? 2Ε6≅Α2;06.9.
E9 2;Β;06.1< Λ=.?. Α<1< 2; P 2Μ ≅2 ?2=?2≅2;Α. 0<:<: (82) (P 2):
A9 .;Α2=<;2? . 9. 3Β;06Ω; =?<=<≅606<;.9 P 2 Β; 0Β.;Α6Η0.1<?, ≅2 1602 >Β2 9. Χ.?6./92 2 5. =.≅.1< . ≅2? 8%4−%&/) /−+%(%.
∗;. =?<=<≅606Ω; 12 9. 3<?:. (82) (P 2) 2≅ Χ2?1.12?. 0Β.;1< Α<1.≅ 9.≅ ≅Β≅Α6ΑΒ06<;2≅ 12 9. Χ.?6./92 2 =<? ΑΤ?:6;<≅ 2≅=20ΥΗ0<≅ 129 0<;7Β;Α< 12 ?232?2;06., 0<;Χ62?Α2; .P 2 2; 2;Β;06.1<
Χ2?1.12?<.
∗; 2;Β;06.1< 12 9. 3<?:. (92) (P 2) 2≅ Χ2?1.12?< 0Β.;1< .9 :2;<≅ Β; 0.≅< 12 ≅Β≅Α6ΑΒ06Ω;
12 9. Χ.?6./92 2 =<? Β; ΑΤ?:6;< 2≅=20ΥΗ0< 129 0<;7Β;Α< 12 ?232?2;06., 0<;Χ62?Α2 . P 2 2; Β; 2;Β;06.1< Χ2?1.12?<.
!.≅ =?<=<≅606<;2≅ Β;6Χ2?≅.92≅ =Β212; .=.?202? ?24.1.≅, 0<:< 2; 29 2;Β;06.1<: Λ#< Α<1<≅ ≅<; :20Ρ;60<≅Μ. E; 2≅Α2 0.≅< 9. ≅6:/<96Γ.06Ω; ≅2?Ρ: (82) (M 2) 1<;12 M 2 2≅ 9. 3Β;06Ω;
=?<=<≅606<;.9 12 Λ22≅ :20Ρ;60<Μ >Β2 Α<:. Χ.9<?2≅ 12;Α?< 129 0<;7Β;Α< 12 ?232?2;06. 3<?:.1< =<? 9<≅ 5<:/?2≅.
!.≅ =.9./?.≅ Λ;6;4Ξ;Μ, Λ;6;4Β;<Μ, Λ;.1.Μ, Λ;.162Μ, 0<??2≅=<;12; Α.:/6Τ; . 2;Β;06.1<≅ Β;6Χ2?≅.92≅ 0<; ;24.06<;2≅, =2?< 12 Β;. :.;2?. 16≅Α6;Α. . 9.≅ =?<=<≅606<;2≅ .;Α2?6<?2≅. !. =?=<≅606Ω; Λ;6;4Β;< 2≅ :20Ρ;60<Μ ;< 2>Β6Χ.92 . 9. =?<=<≅606Ω; Λ;< Α<1<≅ ≅<; :20Ρ;60<≅Μ ≅6;< . 9. 2Ε=?2≅6Ω; Λ=.?. Α<1< 2, 2 ;< 2≅ :20Ρ;60<Μ >Β2 ≅2 ≅6:/<96Γ.(82) (M 2):
Λ2 2≅ Β; 3.;Α.≅:.Μ. A;Ρ9<4.:2;Α2 . 9< >Β2 <0Β??2 0<; 9<≅ 0Β.;Α6Η0.1<?2≅ Β;6Χ2?≅.92≅, 9.≅
=?<=<≅606<;2≅ 2Ε6≅Α2;06.92≅ =Β212; Α2;2? ;24.06<;2≅ 6;Α2?;.≅ 0<:< Λ.94< ;< 2≅ :<?Α.9Μ 9. 0Β.9 ≅2 ≅6:/<96Γ. 0<:< (92) (M 2) 1<;12M 2 ≅6:/<96Γ. 9. 2Ε=?2≅6Ω; Λ2 2≅ :<?Α.9Μ.
O&5)48%∋−21
A≅Υ 0<:< .09.?.:<≅ 2; ≅Β :<:2;Α< 2; 29 0Ρ90Β9< =?<=<≅606<;.9, 29 0Ρ90Β9< 0Β.;Α6Η0.06<;.9 =?2≅2;Α. Α.:/6Τ; Β;. 2≅Α?Β0ΑΒ?. =?<=6., >Β2 .1606<;. . 9.≅ ?249.≅ Φ. 2≅Α./92061.≅ =.?. 29 0Ρ90Β9< ≅2 =?<=<≅606<;2≅,=2?:6Α2 9. 0<;≅<961.06Ω; 129 0<:=927< =2?< :.?.Χ699<≅< Β;6Χ2?≅< 12 9. 9Ω460. 3<?:.9.
C<;≅2?.Χ;1< 9. <?62;Α.06Ω; >Β2 ;<≅ 52:<≅ =?<=Β2≅Α<, 0<;≅612?.:<≅ 6:=<?Α.;Α2 29 0<;<06:62;-Α< 0<:=920<;<06:62;-Α< 12 9. 2≅Α?Β0ΑΒ?. /Ρ≅60., Φ 2; 2≅Α2 ≅2;Α61< =?2≅2;Α.:<≅ 9<≅ 292:2;0<;<06:62;-Α<≅ 3Β;1.:2;-Α.92≅ . 0<;Α6;Β.06Ω;:
(64;<≅ =?6:6Α6Χ<≅ 129 0Ρ90Β9< 0Β.;Α6Η0.06<;.9: 8 (0Β.;Α6Η0.1<? Β;6Χ2?≅.9).
)+/% ∗240%6−8%:(6P 12≅64;. Β;. 3Ω?:Β9.; 2; 9. 0Β.9 ;< Η4Β?. 9. 2Ε=?2≅6Ω;(82);2;Α<;02≅
(82) (P) 12≅64;. Β;. 3Ω?:Β9..
!−+12 ()<1−(2: (6 P 12≅64;. Β;. 3Ω?:Β9., 2; 9. 0Β.9 ;< Η4Β?. (82); 2;Α<;02≅ (92) (P)
12≅64;. 9. 3Ω?:Β9. (82) (P):
1. D6?2:<≅ >Β2 Β;. 3Ω?:Β9. P ;< 2≅ΑΡ 0Β.;Α6Η0.1. /.7< 29 ΑΤ?:6;< 2; ≅6 2; P ;< Η4Β?.
(82) <(92):
2. E; .129.;Α2, 0Β.;1< Β;. 2Ε=?2≅6Ω; Η4Β?2 0Β.;Α6Η0.1., ≅2 ≅</?2 2;Α62;12 >Β2 ≅2 ≅.Α6≅-3.02; 9.≅ 0<;1606<;2≅ ?2>Β2?61.≅.
C7%16−<∋%(24)5 )1 71% /)64% D)5∋4−3∋−Β1 B?5−∋% D2≅0?6/6:<≅ .5<?. 9<≅ </72Α<≅ >Β2 2≅ΑΒ16.?2:<≅.
C<:2;Γ.?2:<≅ =<? .>Β299.≅ 3Β;06<;2≅ =?<=<≅606<;.92≅ >Β2 Α62;2; ≅Ω9< Β;. 6;12Α2?:6;.06Ω;.
F71∋−21)5 342325−∋−21%/)5 )1 71% /)64% ∗;. 3Β;06Ω; =?<=<≅606<;.9 2; 9. 92Α?.22≅ Β;.
2Ε=?2≅6Ω; 3<?:.9 +(2) Α.9 >Β2 ≅2 Α62;2 9< ≅64Β62;Α2: C.1. Χ2Γ >Β2 ≅2 ?2:=9.Γ. 9. 92Α?. 2 =<?
Β; 292:2;Α< a 12 Β; 0<;7Β;Α< (=?2Χ6.:2;Α2) 1.1< U; ?2≅Β9Α. Β;. =?<=<≅606Ω; +(a):
O&5)48%∋−Β1
!. =.9./?. 92Α?. Α62;2 .>ΒΥ Β; ≅2;Α61< ≅6:69.? .9 12 9. =.9./?. Χ.?6./92: Β;. 92Α?. 12/2 6;Α2?=?2Α.?≅2 0<:< Β; 2≅=.06< 2; /9.;0< >Β2 ≅2 =Β212 ?2992;.? 0<; 062?Α<≅ </72Α<≅ Α<:.1<≅ 12 Β; 0<;7Β;Α< 1.1<.
∗≅.?2:<≅ 29 ≅Υ:/<9<Λ:Μ =.?. 12Η;6? 3Β;06<;2≅ =?<=<≅606<;.92≅ (0<:< 2; 29 272:=< . 0<;Α6;-Β.06Ω;).
(6 29 0<;7Β;Α<U 2≅ R Φ +(2) : 2 +2= 5;(2 + = 5), 2;Α<;02≅:
1. +(2)2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9.
2. +(3) : 2 + 3 = 5 Φ+(1) : 2 + 1 = 5 ≅<; =?<=<≅606<;2≅;+(3) 2≅ Χ2?1.12?. Φ+(1) 2≅ 3.9≅..
C7%16−<∋%(24 71−8)45%/ (6+(2)2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 ΦU 2≅ Β;0<;7Β;Α<, 2;Α<;02≅ 9. 2Ε=?2≅6Ω; (822U)+(2) 2≅ Β;. 2Ε=?2≅6Ω; >Β2 ≅64;6Η0. >Β2 .9 ?22:=9.Γ.? 9. 92Α?. 2 =<?
0Β.9>Β62? 292:2;Α< a 12U; ?2≅Β9Α.+(a) Χ2?1.12?..
!. 2Ε=?2≅6Ω;(822U)+(2) ≅2 922; =.?. Α<1< 2 2; (12)U (≅2 0Β:=92)+ 122, 0Β.9>Β62?. ≅2. 2 2; U (≅2 0Β:=92) + 122; 2Α0.
(!20ΑΒ?.≅ :Ρ≅ 6;3<?:.92≅ ≅<; ?20<:2;1.1.≅, <0.≅6<;.9:2;Α2 Φ =.?. 2;Α2;12? :27<? 9. =?<=<≅6-06Ω;. E;0<;Α?.?Ρ .94Β;<≅ 272:=9<≅ 2; 9. ≅2006Ω; 12 272?0606<≅).
(2 Α62;2:
1. (6 U 2≅ R Φ +(2) : 2 +2= 5; 2;Α<;02≅ (822U)+(2) 2≅ 3.9≅..
E; 29 92;4Β.72 5./6ΑΒ.9, 0<??2≅=<;12 . 2≅Α. 3<?:. 12 2Ε=?2≅6<;2≅ Α.92≅ 0<:< )<1<≅ 9<≅ 3.;Α.≅-:.≅ ≅<; 5<9<4?.3.;Α.≅-:.≅, C.1. 1Υ. .=?2;1< .94< ;Β2Χ<, CΒ.9>Β62?. =Β212 0.;Α.?; )<1< 5<:/?2 2≅ :<?Α.9.
C7%16−<∋%(24 )9−56)1∋−%/ (6 +(2) 2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 Φ U 2≅ Β; 0<;7Β;Α<, 2;-Α<;02≅ 9. 2Ε=?2≅6Ω; (922U)+(2) 2≅ Β;. =?<=<≅606Ω; >Β2 ≅64;6Η0. >Β2 .9 :2;<≅ =.?. Β;
292:2;Α< a 12U ≅2 Α62;2 >Β2 +(2) 2≅ Χ2?.12?..
!. 2Ε=?2≅6Ω; (922U)+(2) ≅2 922; 2Ε6≅Α2 (.9 :2;<≅ Β;) 2 (2; U) Α.9 >Β2 + 12 2; 5.Φ (.9
:2;<≅ Β;) 2 (2;U) Α.9 >Β2 +12 2, Φ ≅6:69.?2≅.
(!20ΑΒ?.≅ :Ρ≅ 6;3<?:.92≅ ≅<; ?20<:2;1.1.≅, <0.≅6<;.9:2;Α2 Φ =.?. 2;Α2;12? :27<? 9. =?<=<≅6-06Ω;. E;0<;Α?.?Ρ .94Β;<≅ 272:=9<≅ 2; 9<≅ 272?0606<≅).
(6 U 2≅ R; +(2) : 2 +2= 5; ,(2) : [22 1 = (2+ 1) (2 1)]; −(2) :22 1; 2;Α<;02≅:
1. (922U)+(2);(922U),(2) ≅<; Χ2?1.12?.≅.
2. (922U)−(2)2≅ 3.9≅..
E; 29 92;4Β.72 5./6ΑΒ.9 0<??2≅=<;12 . 2≅Α. 3<?:. 12 2Ε=?2≅6<;2≅ Α.92≅ 0<:< A94Β;<≅ =2??<≅ :Β2?12;, A94Β62; ≅2 0<:6Ω :6 .Χ2;..
1.4.1. )+/%5 3%4% )/ 752
+2?2:<≅ .5<?. .94Β;.≅ ?249.≅ 3Β;1.:2;Α.92≅ =.?. 29 Β≅< 12 9<≅ 0Β.;Α6Η0.1<?2≅. E≅Α.≅ ?2-49.≅ ≅<; 0<;Χ2;06<;.92≅, =2?< 2≅ <=<?ΑΒ;< Α2;2? =?2≅2;Α2 >Β2 299.≅ ?20<42; 29 ≅2;Α61< >Β2 0<:Ξ;:2;Α2 ≅2 1. . 9.≅ 2Ε=?2≅6<;2≅ .;Ρ9<4.≅ 2; 616<:. 2≅=.ς<9, <Α<?4Ρ;1<92≅, 09.?< 2≅ΑΡ, Β;. =?206≅6Ω; :.Φ<?.
%<12:<≅ 1.?;<≅ 272:=9<≅ 12 Χ.?6.1. Υ;1<92 =.?. 0<;Η?:.? 9. 6:=?2≅6Ω; 12 >Β2 2≅Α.≅ ?249.≅ ≅<; /.≅Α.;Α2 ?.Γ<;./92≅
%<? <Α?. =.?Α2, ≅6 ≅2 ;<≅ =?2≅2;Α. .94Ξ; 272:=9< 2; 29 >Β2 Β;. 12 2≅Α.≅ ?249.≅ ?2≅Β9Α2 =<0< ?.Γ<;./92, 2;Α<;02≅ =?</./92:2;Α2 5.?Υ.:<≅ /62; 2; ./.;1<;.?9..
A≅Υ, .Ξ; 0Β.;1< ;< 1.?2:<≅ 7Β≅Α6Η0.06Ω; 12 9.≅ ?249.≅ (129 :6≅:< :<1< >Β2 ;< 2≅ ;202≅.?6< 7Β≅Α6Η0.? 9.≅ ?249.≅ 12 Β; 7Β24< 0<:< 29 .721?2Γ < Β;< 12 ;.6=2≅), :2;06<;.?2:<≅ 2Ε=?2≅.-:2;Α2 .94Β;.≅ 2Ε=?2≅6<;2≅ >Β2 ;< ≅2?Υ. 0<;Χ2;62;Α2 .02=Α.? 0<:< ?249.≅.
A 0<;Α6;Β.06Ω; 12 0.1. ?249.≅ >Β2 =?2≅2;Α.?2:<≅ 5.?2:<≅ Β; 0<:2;Α.?6< 12 9<;46ΑΒ1 Χ.?6./92. %.?. Β;. ?232?2;06. :Ρ≅ 2Ε=216Α., 52:<≅ ?2Β;61< 9.≅ ?249.≅ 2; Β; 0Β.1?< .9 Η;.9 12 2≅Α2 0.=ΥΑΒ9<.
O&5)48%∋−Β1
#< ≅<:<≅ 0.=.02≅ 12 2;3.Α6Γ.? 2; :<1< ≅ΒΗ062;Α2 0ΒΡ; 6:=<?Α.;Α2 ≅<; 9.≅ ?249.≅ 2 Φ 3 Φ 9.
?249. 8 (>Β2 2≅, 2; ?2.961.1, Β; Α2<?2:.). !.≅ <Α?.≅, =<? 29 0<;Α?.?6<, ;< ≅2?Ρ; Β≅.1.≅ 0<;
3?20Β2;06. =<? .5<?. Φ =Β212 922?9.≅ 0<; 12Α2;06Ω;, 0<:=?2;12?9.≅ Φ Χ<9Χ2? =<≅Α2?6<?:2;Α2 ≅</?2 299.≅.
E; Α<1. 2≅Α. ≅2006Ω;,U 2≅ Β; 0<;7Β;Α< 12 ?232?2;06.;+(2); ,(2)≅<; 3Β;06<;2≅ =?<=<≅606<;.92≅, .;<Α.?2:<≅(82)+(2)=.?. 2Ε=?2≅.?(822U)+(2)Φ(92)+(2)=.?. 2Ε=?2≅.?(922U)+(2):
)+/% 1
R1: (82)+(2) =)(92)+(2) (U 6=)
C<:< ≅2 Χ2 2≅ /.≅Α.;Α2 ?.Γ<;./92.
H2:<≅ .ς.161< >Β2 29 0<;7Β;Α< U Α2;4. .9 :2;<≅ Β; 292:2;Α< (2; 0.≅< 0<;Α?.?6< Φ ≅24Ξ; =Β212 0<:=?</.? =<≅Α2?6<?:2;Α2, 12 =?232?2;06. 0Β.;1< 5.Φ. Χ6≅Α< 0<;7Β;Α<≅, ≅2 Α62;2 >Β2
(82)+(2) 2≅ Χ2?1.12?. Φ >Β2(92)+(2)2≅ 3.9≅.).
)+/% 2
R2:(82)+(2) () (92)+(2)
!. ?249. 6;160. 09.?.:2;Α2 >Β2 =.?. 9. 2Ε=?2≅6Ω; (82)+(2) ≅2. Χ2?1.12?., ;< 12/2 5./2? 2Ε02=06Ω; .94Β;., =Β2≅ Α.9 2Ε02=06Ω; 9. 6;Χ.961.?Υ., .9 5.02? Χ2?1.12?. ≅Β ;24.06Ω;.
!. ?249. =Β212 2Ε=?2≅.?≅2 16062;1< >Β2 9. 3.9≅21.1 12 9. 2Ε=?2≅6Ω; (82)+(2) ≅2 12:Β2≅Α?.
0<; Β; 0<;Α?.-272:=9<: Β; 292:2;Α< 2 12U =.?. 29 0Β.9+(2)2≅ 3.9≅., (2≅ 1206?, =.?. 29 0Β.9
+(2) 2≅ Χ2?1.12?..
!< >Β2 .Η?:. 2≅Α. ?249. 2≅ >Β2 0Β.;1< 1206:<≅ ≅62:=?2 >Β2?2:<≅ 1206? ≅62:=?2 (Φ ;< 0.6 ≅62:=?2, < 9. :.Φ<?Υ. 12 9.≅ Χ202≅, < ;< ≅2 Α62;2 ;<Α606. 12 >Β2 ≅2. 3.9≅., 2Α0. ), 0Β.;1< 1206:<≅ Α<1< >Β2?2:<≅ 1206? Α<1< (Φ ;< 0.≅6 Α<1<, 29 99;99 % 12 9.≅ Χ202≅, =.?202 >Β2 Α<1<, =.?. >Β2
;<≅ Χ.:<≅ . 5.02? =?</92:., 2Α0.).
(6 ≅2 Α?.Α.?. 12 =?</.? >Β2 9. .Η?:.06Ω; #< 2≅ 062?Α< >Β2 Α<1<≅ 9<≅ <≅<≅ ≅<; /9.;0<≅ 2≅ Χ2?1.12?., /.≅Α.?Υ. 0<; 2Ε56/6? Β; <≅< >Β2 ;< ≅2. /9.;0<.
!. .Η?:.06Ω; )<1< ;Ξ:2?< ?2.9 Α62;2 Β; 6;Χ2?≅< :Β9Α6=960.Α6Χ< Α62;2 Β;. (Ξ;60.) 2Ε02=06Ω;, Φ 2≅ =<? 9< Α.;Α<, 6??216:6/92 Φ 1206161.:2;Α2 3.9≅..
[](+2. 2≅Α2 272:=9<, :Ρ≅ ≅ΒΑ69, :Ρ≅ .129.;Α2). (Β=<;4. >Β2 Β; 5<:/?2 12 60 .ς<≅ 120612
2≅0?6/6? ≅Β≅ :2:<?6.≅,. #< Α62;2 2Ε=2?62;06. ;6 .=?2;12, 12 :<1< >Β2 12:<?. Β; .ς< 2; 2≅0?6/6? Β; .ς< 12 ≅Β Χ61.; (9.≅ :2:<?6.≅ 0.1. Χ2Γ :Ρ≅ ./Β??61.≅). (Β=<;4. >Β2 2≅2 5<:/?2 ;< :Β2?2, Π2≅0?6/6?Ρ Α<1.≅ ≅Β≅ :2:<?6.≅? ((6 ≅2 >Β62?2 =?</.? >Β2 ;<, 5.Φ >Β2 2;0<;Α.? .94Β;., 2; .94Ξ; .ς<, >Β2 ;< 9<4?. ?29.Α.?. A>ΒΥ ;<≅ 6;Α2?2≅. ≅Ω9< 9. 9Ω460. 129 =?</92:. Φ ;< 9.≅ 2Χ2;ΑΒ.92≅ 16Η0Β9Α.12≅ =?Ρ0Α60.≅ ).
O&5)48%∋−Β1
)?.1Β061. .9 2≅=.ς<9, 9. 2Ε=?2≅6Ω; (82)+(2) =Β212 922?≅2 Λ∃% )ie#&(e )e ∗ie∃e &(2)Μ, Α.9
.Η?:.06Ω; 2≅ 16≅Α6;Α. 12 (82)+(2), >Β2 =Β212 922?≅2 Λ∃+∃ca )e ∗ie∃e &(2)Μ.
AΞ; 0Β.;1< 2≅ 2Χ612;Α2 >Β2 .:/.≅ 2Ε=?2≅6<;2≅ .Η?:.; 0Β2≅Α6<;2≅ 16≅Α6;Α.≅, 2; 29 Β≅< 16.?6< ;< ≅Β292 :.?0.?≅2 9. 1632?2;06..
!. 3?.≅2 #< Α<1< 9< >Β2 /?699. 2≅ <?< 0<??2≅=<;12 . Β;. 2Ε=?2≅6Ω; 129 Α6=< (82)+(2):
%<? <Α?. =.?Α2, 9. 2Ε=?2≅6Ω; ")<1< 9< >Β2 /?699. ;< 2≅ <?< .Η?:. >Β2 ;.1. >Β2 /?6992 2≅ <?< Φ ≅Β 2≅Α?Β0ΑΒ?. 2≅ (82)+(2):
!< >Β2 2≅Α<≅ Ξ9Α6:<≅ 272:=9<≅ :Β2≅Α?.; 2≅ >Β2 ;< ≅Ω9< =<12:<≅ ≅2? 6:=?206≅<≅ 2; 29 92;4Β.72, ≅6;< >Β2 6;09Β≅< =<12:<≅ 5./2?;<≅ Λ0<;Α.:6;.1<Μ 12 Β; :<1< 12 =2;≅.? 6;.=?<=6.1<.
)+/% 3
R3:(92)+(2) () (82)+(2)
E≅Α. ?249. 1209.?. 0Ω:< ≅2 =?Β2/. >Β2 .94Β;. =?<=621.1 ;< 2≅ 062?Α., ;Β;0., 7.:Ρ≅.
E99. =<;2 12 :.;6Η2≅Α< 9< 163Υ069 >Β2 =Β212 ?2≅Β9Α.? 9. 12:<≅Α?.06Ω; 12 062?Α.≅ .Η.:06<;2≅. C<;≅612?2 .9 ?2≅=20Α<, 9.≅ 3?.≅2≅ E≅ 6:=<≅6/92 ≅.0.?≅2 29 05.920< ≅6; ≅.0.?≅2 9. 05.>Β2Α., #< 2Ε6≅Α2; 9<≅ =9.Α699<≅ Χ<9.1<?2≅; #< 5.Φ :.9 >Β2 1Β?2 062; .ς<≅.
E; 42;2?., Β;< =<1?Υ. =2;≅.? >Β2 Β;. .Η?:.06Ω; 129 Α6=< (92)+(2) ;< 2≅ 3Ρ069 12 =?</.?; Α.9 12:<≅Α?.06Ω; 12/2?Υ. 0<;Χ2;02? >Β2 ;6;4Ξ; </72Α< >Β2 . .94Β62; ≅2 92 =Β162?2 <0Β??6? 0Β:=96?Ρ +(2) (Φ .Ξ; 299< ;< ≅2?Υ. ≅ΒΗ062;Α2).
E; <Α?.≅ =.9./?.≅, 9. ?249.≅ 6;160. >Β2 Α.; 163Υ069 =Β212 ≅2? =?</.? >Β2 .94< ;< =Β212 <0Β??6?; 2; 2≅Α2 ≅2;Α61<, 0Β.;1< .>ΒΥ 1206:<≅ ;Β;0., >Β2?2:<≅ 1206? ;Β;0. (Φ ;< =.?202 >Β2 ;Β;0., ;< ≅2 5. Α2;61< ;<Α606. 12 >Β2, 2; ?2.961.1 ;< 0?2<, Α<1<≅ =62;≅.; >Β2 ;<, 2Α0.).
)+/% 4
R4 : (82) [+(2)^,(2)] () (82)+(2)^(82),(2)
E≅Α. ?249. ≅2 ≅Β292 2Ε=?2≅.? 16062;1< 8 16≅Α?6/ΒΦ2 2;^.
(2 Α?.Α. 12 Β;. ?249. >Β2 =<12:<≅ =?<0212? . <9Χ61.? 2≅ 1206?, Β≅.?9. ≅6; =?2≅Α.?92 :.Φ<? .Α2;06Ω; : A>ΒΥ 2≅Α.:<≅ ≅Ω9< 1209.?.;1< >Β2 ;< 5.Φ >Β2 =?2<0Β=.?≅2 12 2≅Α2 .≅Β;Α<, >Β2
≅2 =Β212 Β≅.? 9. ?249. 0<; Α<1. Α?.;>Β6961.1.
)+/% 5
R5 : (92) [+(2)_,(2)] () (92)+(2)_(92),(2)
+.92 =.?. 299. 9< 0<:2;Α.1< =.?. 9. ?249. .;Α2?6<?.
)+/% 6
R6: (82)+(2)_(82),(2) =)(82) [+(2)_,(2)]
%<? <=<≅606Ω; . 9.≅ 1<≅ .;Α2?6<?2≅, 2≅Α. ?249. ;< 2≅ Β;. 2>Β6Χ.92;06., ≅6;< ≅Ω9< Β;. 6:=960.06Ω;. D2 5205<, ≅2?Υ. ?.Γ<;./92 =<;2?9. 0<:< 2>Β6Χ.92;06., =Β2≅ 2;Α<;02≅ 12/2?Υ. ≅2? ≅62:=?2 062?Α< >Β2 (82) [+(2)_,(2)] =)(82)+(2)_(82),(2); 9< >Β2 12Η;6Α6Χ.:2;Α2 ;< ≅2?Υ. 12 2≅=2?.?
≅6 2;0<;Α?.:<≅ 2; >Β2 29 .;Α20212;Α2 ≅2. Χ2?.1212?< Φ 29 0<;≅20Β2;Α2 3.9≅< (Φ =< 9< Α.;Α<, 9. 6:=960.06Ω; Α.:/6Τ; ≅2. 3.9≅.).
%.?. Α.9 2320Α< 0<:=?Β2/2 >Β2 2; Z : 9. .Η?:.06Ω; )<1< ;Ξ:2?< 2≅ =.? < 6:=.? 2≅
Χ2?-1.12?., =2?< )<1< ;Ξ:2?< 2≅ =.? < /62; Α<1< ;Ξ:2?< 2≅ 6:=.? 2≅ 3.9≅., (=Β2≅ ;6;4Β;. 12 ≅Β≅ 0<:=<;2;Α2≅ 2≅ Χ2?1.12?.).
)+/% 7
R7: (92) [+(2)^,(2)] =)(92)+(2)^(92),(2)
C<; ?2≅=20Α< . 2≅Α. ?249., 9. ≅6ΑΒ.06Ω; 2≅ .;Ρ9<4. . 9. 12 9. .;Α2?6<?, ≅6 /62; .>ΒΥ 9. 6:=960.06Ω; 2≅Α. Λ2; 9. <Α?. 16?2006Ω;Μ.
(6 ≅2 .≅Β:62?. >Β2 ≅2 Α62;2 Β;. 2>Β6Χ.92;06., ≅2 Α2;1?Υ. 2;Α<;02≅ >Β2
(92)+(2)^,(2) =)(92) [+(2)^(92),(2)]
≅2?Υ. ≅62:=?2 Χ2?1.12?..
%<12:<≅ 0<;≅Α?Β6? Β; 0.≅< 2; >Β2 2≅Α. Ξ9Α6:. .Η?:.06Ω; ?2≅Β9Α. 3.9≅. 0<; 9.≅ :6≅:.≅ =?<=<≅6-06<;2≅ Φ 0<;7Β;Α< >Β2 Β≅.:<≅ =.?. 9. ?249. .;Α2?6<?.
)+/% 8
R8 :(82) [+(2) =),(2)] () (92)h+(2)^,(2)i
(2 Α62;2 ≅Β02≅6Χ.:2;Α2
(82) [+(2) =),(2)] () (92) [+(2)^,(2)]
() (92)h+(2)_,(2)i
() (92)h+(2)^,(2)i () (92)h+(2)^,(2)i
1.4.2. C7%16−<∋%(24)5 ∋21 8%4−%5 8%4−%&/)5 D)5∋4−3∋−Β1 B?5−∋%
E; ?2.961.1 ≅2 Α?.Α. .>ΒΥ 12 9<≅ :6≅:<≅ 0Β.;Α6Η0.1<?2≅ >Β2 2; 9. =?6:2?. =.?Α2, =2?< .5<?. ?232?61<≅ . 3Β;06<;2≅ =?<=<≅606<;.92≅ 2; :Ρ≅ 12 Β;. 92Α?..
(6 2; Β;. 2Ε=?2≅6Ω; .=.?202 :Ρ≅ 12 Β;. Χ.?6./92 96/?2, =<12:<≅ Β≅.? :Ρ≅ 12 Β; 0Β.;Α6Η0.1<?.
E; 9. 2Ε=?2≅6Ω;3=22+225.Φ 1<≅ Χ.?6./92≅ 96/?2≅. A5<?. ≅6 0<;≅612?.:<≅(83) (93) (3 22+ 22= 0)
2≅ Β;. .Η?:.06Ω; Χ2?1.12?., =Β2≅ =.?. 0Β.9>Β62? 2 >Β2 ≅2 Α<:2 (?2.9) =Β21< 2;0<;Α?.? Β;3
>Β2 ≅.Α6≅3.02 9. 20Β.06Ω;. (6; 2:/.?4<, 1605. .Η?:.06Ω; ;< 2≅ 9< :6≅:< >Β2(93) (83) (3 22 + 22= 0)
>Β2 1602 >Β2 2Ε6≅Α2 Β;3>Β2 ≅6?Χ2 =.?. Α<1<2>Β2 Φ< Α<:2, 09.?.:2;Α2 9. .Η?:.06Ω; 2≅ 3.9≅..
!. 0<;09Β≅6Ω; 129 272:=9< .;Α2?6<?: E9 <?12; 12 9<≅ 0Β.;Α6Η0.1<?2≅ ≅Υ 6:=<?Α. Φ 2≅ Β; 2??<? :ΒΦ 0<:Ξ; 0.:/6.? ≅Β <?12;.
CΒ.;1< 5.Φ 1<≅ 0Β.;Α6Η0.1<?2≅ .=.?202;80<:/6;.06<;2≅. A94Β;.≅ 0<:/6;.06<;2≅ ≅<;
2>Β6Χ-.92;Α2≅ =2?< <Α?.≅ ;<. !< Χ2:<≅ 2; 29 0Β.1?< ≅64Β62;Α2. (2. P (2c3) Β;. 2Ε=?2≅6Ω; 0<; 1<≅ Χ.?6./92≅ 96/?2≅.
(82) (83)P (2c3) () (83) (82)P(2c3)
+ +
(92) (83)P (2c3) (93) (82)P(2c3)
+ +
(83) (92)P (2c3) (82) (93)P(2c3)
+ +
(93) (92)P (2c3) () (92) (93)P(2c3)
C<;≅612?2 9. Α./9. .;Α2?6<? 0<; 9< ≅64Β62;Α2: %<≅6/92≅ Χ.9<?2≅ 12 2 ≅<; Α<1<≅ 9.≅ =2?≅<;.≅,
#<ΑΤ≅2 >Β2 ≅6 5Β/Υ2?. :Ρ≅ Χ.?6./92≅ 5./?Υ. :Β05<≅ :Ρ≅ 0.≅<≅. CΒΡ;Α<≅ 0.≅<≅ 5.Φ ≅6 ≅2 Α62;2;
3 Χ.?6./92≅?.
O&5)48%∋−Β1:
E≅ 6;Α2?2≅.;Α2 :6?.? 9. 0Β2≅Α6Ω; 12 =?<=<≅606<;2≅ Φ 3Β;06<;2≅ =?<=<06<;.92≅ 2; 0<;7Β;Α<. !< 5.02:<≅ . Α?.ΧΤ≅ 12 Β; 272:=9< ≅6:=92 Φ Β; Α.;Α< ?2=2Α61<, =2?< Α<:.?Ρ ≅Ω9< Β; =.? 12 :6;ΒΑ<≅:
(6 Η7.:<≅, =<? 272:=9< R 0<:< 0<;7Β;Α< (Ξ;60<) 12 ?23?2;06., Α2;2:<≅ >Β2: 1. +: 2 + 3 = 5; , : 2 + 3 = 6 ≅<; =?<=<≅606<;2≅, Φ
1: +2≅ Χ2?.12?., 2: , 2≅ 3.9≅..
2. +(2) :2+ 3 = 5 2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 2; Β;. 92Α?. Φ
1: +(2) ;< 2≅ Χ2?1.12?. ;6 3.9≅.,
2: (82)+(2)2≅ 3.9≅., (Α<:.? 2= 5; =<? 272:=9<, 3: (92)+(2)2≅ Χ2?1.12?., (Α<:.? 2= 2).
3. +(2; 3) :2+3= 5 2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 2; 1<≅ 92Α?.≅ Φ
1: +(2; 3) ;< 2≅ Χ2?1.12?. ;6 3.9≅. (;< 2≅ Β;. =?<=<≅606Ω;), 2: (82) (83)+(2; 3)2≅ Β;. =?<=<≅606Ω; 3.9≅.,
3: (92) (83)+(2; 3)2≅ Β;. =?<=<≅606Ω; 3.9≅.,
4: (82) (93)+(2; 3)2≅ Χ2?1.12?. (1.1<2=a; Α<:.? 3= 5 a),
5: (92) (93)+(2; 3)2≅ Χ2?1.12?. (Α<:.?, =<? 272:=9< < .9 .Γ.?, 2= 2 Φ 9Β24< 3= 3) 4. +(2; 3; 4) :2+3=4 2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 2; Α?2≅ 92Α?.≅.
1.4.3. N)+%1(2 %<40%∋−21)5 ∋21 C7%16−<∋%(24)5
#24Β2:<≅ Μ)<1< .9Β:;< 2; 2≅Α2 ≅.9Ω; Α62;2 0./299< ;24?<Μ. %.?. 299< /.≅Α. 1206? ΜEΕ6≅Α2 Β; .9Β:;< 2; 2≅Α2 ≅.9Ω; >Β2 ;< Α62;2 0./299< ;24?<Μ.
∃/≅Τ?Χ2≅2 >Β2 =.?. ;24.? 29 =?6:2? 272:=9<, ;< 2≅ ;202≅.?6< 1206? >Β2 Α<1< .9Β:;< 2; 2≅Α2 ≅.9Ω; ;< Α62;2 29 0./299< ;24?<, >Β2 ≅6:/Ω960.:2;Α2 ≅2?Υ.(82) (P(2)):E≅ 1206?(82) (P (2))
;< 2≅ 9< :6≅:< >Β2 (92) (P (2)):
(6:69.?:2;Α2, ;24.? >Β2 ΜEΕ6≅Α2 Β; .9Β:;< 0<; 0./299< :<?.1<Μ 2≅ 2>Β6Χ.92;Α2 . 1206? >Β2 Μ)<1<≅ 9<≅ .9Β:;<≅ ;< Α62;2; 29 0./299< :<?.1<Μ.
!. 09.Χ2 2≅ (92)P (2) () (82) (P (2)): − ;< 2≅Α.?Υ. /62; ;24.1< 1206? >Β2 ΜEΕ6≅Α2 Β; .9Β:;< >Β2 ;< Α62;2 29 0./299< :<?.1<Μ.
1.4.4. N)+%1(2 %<40%∋−21)5 ∋21 0?5 () 71 ∋7%16−<∋%(24 #24Β2:<≅ 9. .Η?:.06Ω; [(82) (92)P (2c3)]: H.4Ρ:<≅9< =<? =.≅<≅:
(82) (92)P(2c3) () (92) ((93)P (2c3)) () (92) (83) (P (2c3)):
C21∋/75−Β1: %.?. ;24.? .Η?:.06<;2≅ >Β2 6;Χ<9Β0?.; 0Β.;Α6Η0.1<?2≅, 2≅Α<≅ ≅2 0.:/6.; 2;Α?2 ≅Υ, ≅6; 0.:/6.? 9.≅ Χ.?6./92≅ Φ 9. 2Ε=?2≅6Ω; Η;.9 ≅2 ;624. .≅Υ:
(83) (91) (82) (8()3+12+2=( () (93) (81) (92) (9()3+12 26=(:
%<? ≅Β=Β2≅Α<, ≅6 2≅0?6/6:<≅+(2; 3); 2=Β212 Α<:.? Χ.9<?2≅ 2; Β; 0<;7Β;Α<U;23 (Α.9 Χ2Γ) 2;
<Α?< 0<;7Β;Α< V.
I9Β≅Α?.?2:<≅ 9. ≅6ΑΒ.06Ω; .;Α2?6<?:
1. +(2; 3) :23 2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 2; 1<≅ 92Α?.≅ >Β2 =Β212; Α<:.? Χ.9<?2≅ 2; R.
2. ,(2; 3; 4) : 2+3 = 4 2≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 12 Α?2≅ 92Α?.≅ >Β2 =Β212; Α<:.? Χ.9<?2≅ 2; R: (E≅ 09.?< >Β2, .>ΒΥ, ≅6 2 2 3 Α<:.; Χ.9<?2≅ 2;R, 2;Α<;02≅4 ;< ≅2?Ρ, =<?
272:=9<, Β; Α?6Ρ;4Β9<).
3. I;3<?:.9:2;Α2,−(2; 3) :2=.≅. =<?32≅ Β;. 3Β;06Ω; =?<=<≅606<;.9 2; 1<≅ 92Α?.≅, 1<;12
2 Α<:. Χ.9<?2≅ 2; Β; 0<;7Β;Α< 12 ?20Α.≅, 2 3 Α<:. Χ.9<?2≅ 2; Β; 0<;7Β;Α< 12 =Β;Α<≅
(129 =9.;< 5./6ΑΒ.9, ≅6 ≅2 >Β62?2).
1.4.5. )+/%5 3%4% )/ 752
%?<0212?2:<≅ 0<:< 5606:<≅ =.?. 9<≅ 0Β.;Α6Η0.1<?2≅ 2; Β;. 92Α?.: 6?2:<≅ 2;Β;06.;1< Φ 0<-:2;Α.;1< ≅Β02≅6Χ.:2;Α2 ;Β2≅Α?.≅ ?249.≅, >Β2 =2?≅6≅Α6:<≅,=<?Η.1.:2;Α2, 2; 99.:.? .Ε6<;.≅. A≅Β:6:<≅ Β; 0<;7Β;Α< 12 ?232?2;06. U =.?. 9. 92Α?. 2 Φ Β; 0<;7Β;Α< V =.?. 9. 92Α?. 3; (9<
>Β2 Α.:/6Τ; =Β212 2Ε=?2≅.?≅2 16062;1< >Β2 29 =.?(2; 3) Α<:. Χ.9<?2≅ 2; 29 0<;7Β;Α<UV). C<;Χ2;6:<≅ >Β2
(82) (83)+(2; 3) ≅64;6Η0. (822U) (832V)+(2; 3) (92) (83)+(2; 3) ≅64;6Η0. (922U) (832V)+(2; 3); /c:
)+/% 9
R9: (82) (83)+(2; 3) () (82) (83)+(2; 3)
E≅Α. ?249. 6;160. >Β2 ≅6 5.Φ 1<≅ 0Β.;Α6Η0.1<?2≅ Β;6Χ2?≅.92≅ ≅24Β61<≅, ;< 6:=<?Α. 29 <?12; 2; 29 >Β2 ≅2 2≅0?6/.;.
)<:2 ;<Α. 12 2≅Α< Φ ;< ≅2 5.4. =?</92:.≅ 0Β.;1< 92 .=.?2Γ0. Β;. 2Ε=?2≅6Ω; ≅6:69.? :
E≅< 2≅ Α<1<.
)+/% 10
R10: (92) (93)+(2; 3) () (92) (93)+(2; 3) %.?. 2≅Α. ?249. Χ.92 29 :6≅:< 0<:2;Α.?6< >Β2 =.?. 9. .;Α2?6<?.
)+/% 11
R11: (82) (83)+(2; 3) () (92) (83)+(2; 3) ; (U 6=)
(%<1?Υ. 0<;≅612?.?≅2 >Β2 2≅Α. ?249. 2≅ Β;. 2≅=2062 12 0<;≅20Β2;06. ;.ΑΒ?.9 12 9. ?249. 1).
(%<? ≅Β=Β2≅Α<, =<1?Υ.:<≅ 5./2? 2≅0?6Α<(82) (83)+(2; 3) () (92) (83)+(2; 3);=2?< 52:<≅
1. (6:/<96Γ.? 9<≅ ≅64Β62;Α2≅ 2;Β;06.1<≅: a) )<1< 2≅ =2?20212?<.
b) H.Φ :.?06.;<≅.
c) A94Β62; ;< 2≅ =2?320Α<. d) #< 5.Φ 0<≅.≅ ≅Ω961.≅.
e) (6 Α<1< 2≅ ?<7<, 5.Φ .94< ?<7<. f) #.1. ≅2 :Β2Χ2.
g) #< Α<1< 2≅ =2?320Α<. h) #.1. 2≅ =2?20212?<.
2. I;160.?, 0<; /.≅2 2; 9.≅ ?249.≅ 3<?:.Α6Χ.≅ 2≅Α./92061.≅ 2; 29 0Ρ90Β9< 12 =?<=<≅606<;2≅ Φ 9. Ξ9Α6:. ?249. .;<Α.1. =.?. 29 0Ρ90Β9< 12 0Β.;Α6Η0.1<?2≅, 0ΒΡ92≅ 12 9.≅ ≅64Β62;Α2≅ 2Ε=?2≅6<;2≅ ≅<; 3Ω?:Β9.≅:
a) (2=3) =)((82) ( (2=3)))
b) (82) (22A=)22B)
c) (82) (22A)_(82) (22B)
d) (82) (22A_(82) (22B))
e) (82) ((2=4)^(83) (32B))
f) (82) (83) ((0=3) =)(3=2))
g) (82) ((83) (4 2U))
3. (2.;:
a) P 2: (22A) =)(22A_22B)
b) Q2: (2=/^22B) =)(/2B)
