Math bac ex 11 (1) by abdelilahe

.2010/2009

:Δϴγ΍έΪϟ΍ ΔϨδϟ΍

νέϷ΍ ϭ ΓΎϴΤϟ΍ ϡϮϠϋ ϙΎΑ 2

:ϯϮΘδϤϟ΍

3 )FFFFFd29 ( 1)H9 k ?(?S2b( §FFFFlA)d2b( pFFFFFFbHbH

.ΔϨϜϤϤϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ Ϯϫ Ύϣ (1 .2 ϱϭΎδϳ ΔΑϮΤδϤϟ΍ Ε΍ήϜϟ΍ ϡΎϗέ΃ ωϮϤΠϣ ΎϬϴϓ ϥϮϜϳ ϲΘϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ Ϯϫ Ύϣ (2

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 07

.˯΍ΩϮγ Ε΍ήϛ 3 ˯΍ήϤΣ Ε΍ήϛ 3 ϭ ˯ΎπϴΑ Γήϛ ϰϠϋ ϕϭΪϨλ ϱϮΘΤϳ .ϕϭΪϨμϟ΍ Ϧϣ Ε΍ήϛ 3 Ύϴϧ΂Η ϭ Ύϴ΋΍Ϯθϋ ΐΤδϧ ΎϬΗίήϓ΃ ϲΘϟ΍ ϥ΍ϮϟϷ΍ ΩΪόΑ ΔΒΤγ Ϟϛ ςΑήϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ X ϦϜϴϟ .ΔΒΤδϟ΍ ϩάϫ . X ΎϫάΧ΄ϳ ϥ΃ ϦϜϤϳ ϲΘϟ΍ ϢϴϘϟ΍ ΩΪΣ (1 . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ϝΎϤΘΣ΍ ϥϮϧΎϗ ΩΪΣ (2

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 08 2 ; 2 ; 2 ;1;1;1;0 ; 0 ; 0 :ϲϟΎΘϟΎϛ ΔϤϗήϣ ΕΎϗΪϴΑ 9 ϰϠϋ βϴϛ ϱϮΘΤϳ .βϴϜϟ΍ Ϧϣ ΕΎϗΪϴΑ ΙϼΛ ΪΣ΍ϭ ϥ΁ ϲϓ ϭ Ύϴ΋΍Ϯθϋ ΐΤδϧ (1 :ϦϴϴϟΎΘϟ΍ ϦϴΗΪΤϟ΍ Ϧϣ Ϟϛ ϝΎϤΘΣ΍ ΐδΣ΃ ."ΎϴΟϭί ΎϤϗέ ϞϤΤΗ ςΒπϟΎΑ ΓΪΣ΍ϭ ΔϗΪϴΑ ΪΟϮΗ ΔΑϮΤδϤϟ΍ ΕΎϗΪϴΒϟ΍ ϦϴΑ Ϧϣ" : E 1

."1 Ϣϗήϟ΍ ϞϤΤΗ ϞϗϷ΍ ϰϠϋ ΓΪΣ΍ϭ ΔϗΪϴΑ ΪΟϮΗ ΔΑϮΤδϤϟ΍ ΕΎϗΪϴΒϟ΍ ϦϴΑ Ϧϣ" : E 2 Ϧϣ ϦϴΘϗΪϴΑ ϝϼΣ· ϥϭΪΑ ϭ ϊΑΎΘΘϟΎΑ Ύϴ΋΍Ϯθϋ ΐΤδϧ ΓήϤϟ΍ ϩάϫ ϲϓ (2 .βϴϜϟ΍ .ϦϴΘΑϮΤδϤϟ΍ ϦϴΘϗΪϴΒϟ΍ ϲϤϗέ ωϮϤΠϣ ϱϭΎδϳ ϱάϟ΍ ήϴϐΘϤϟ΍ X ϦϜϴϟ . X ΎϫάΧ΄ϳ ϲΘϟ΍ ϢϴϘϟ΍ ΩΪΣ (΃ . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ϝΎϤΘΣ΍ ϥϮϧΎϗ ΩΪΣ (Ώ . V X ΓήϳΎϐϤϟ΍ ϭ E X ϲοΎϳήϟ΍ ϞϣϷ΍ ΐδΣ΃ (Ν

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 09 10 Ϧϣ ΔϧϮϜϣ ΔΌϓ :ΕΎΌϓ ΙϼΛ ϰϠϋ ϦϴϋίϮϣ ΍άϴϤϠΗ 20 Ϧϣ Ϣδϗ ϥϮϜΘϳ 6 Ϧϣ ΔϧϮϜϣ ΔΌϓ ϭ ˬ ϦϴϴΟέΎΧ άϴϣϼΗ 4 Ϧϣ ΔϧϮϜϣ ΔΌϓ ϭ ˬ ϦϴϴϠΧ΍Ω άϴϣϼΗ . ϦϴϴϠΧ΍Ω ϒμϧ άϴϣϼΗ φΤϟ΍ βϔϧ άϴϤϠΗ ϞϜϟ ϥ΃ νήΘϔϧ .ϢδϘϟ΍ ϞϴΜϤΘϟ άϴϣϼΗ 3 Ϧϣ ΔϨΠϟ ϦϳϮϜΗ Ϊϳήϧ .ΔϨΠϠϟ΍ ϲϓ ΍Ϯπϋ ϥϮϜϳ ϲϜϟ .ΔϨΠϠϟ΍ ϞΧ΍Ω ΔϠΜϤϤϟ΍ ΕΎΌϔϟ΍ ΩΪϋ ϱϭΎδϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ X ϦϜϴϟ . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ΎϫάΧ΄ϳ ϲΘϟ΍ ϢϴϘϟ΍ ΩΪΣ (1 . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ϝΎϤΘΣ΍ ϥϮϧΎϗ ςϋ΃ (2 . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϠϟ ϲοΎϳήϟ΍ ϞϣϷ΍ ΐδΣ΃ (3

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 10 Ϧϣ Ύϴ΋΍Ϯθϋ ΐΤδϧ .7 ϰϟ· 1 Ϧϣ ΔϤϗήϣ ΕΎϗΪϴΑ 7 ϰϠϋ βϴϛ ϱϮΘΤϳ .ϝϼΣ· ϥϭΪΑ ϭ ϊΑΎΘΘϟΎΑ ΕΎϗΪϴΒϟ΍ ˬβϴϜϟ΍ ΐΤδϟ΍ ϲϓ ϲΟϭί Ϣϗέ ϰϠϋ Γήϣ ϝϭϷ ϝϮμΤϟ΍ ϝΎϤΘΣ΍ Ϯϫ Ύϣ (΃ (1 ˮΚϟΎΜϟ΍ ϱΩήϓ Ϣϗέ ϭ ϦϴϴΟϭί ϦϴϤϗέ ϰϠϋ ϝϮμΤϟ΍ ϝΎϤΘΣ΍ Ϯϫ Ύϣ (Ώ ˮϰϟϭϷ΍ ΙϼΜϟ΍ ΕΎΒΤδϟ΍ ϝϼΧ ΎϤϗέ ϞϤΤΗ ϲΘϟ΍ ΕΎϗΪϴΒϟ΍ ΩΪϋ ϱϭΎδϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ϡ X ϦϜϴϟ (2 .ΎϳΩήϓ ΎϤϗέ ϞϤΤϳ ϕΪϴΒϟ Γήϣ ϝϭϷ έϮϬψϟ΍ ϞΒϗ ΔΑϮΤδϤϟ΍ ϭ ΎϴΟϭί . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ϝΎϤΘΣ΍ ϥϮϧΎϗ ςϋ΃ (΃ . E X ϲοΎϳήϟ΍ ϞϣϷ΍ ΐδΣ΃ (Ώ

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 11

5 ϰϟ· 1 Ϧϣ ΔϤϗήϣ ˯΍ήϤΣ Ε΍ήϛ βϤΧ ϰϠϋ A ϕϭΪϨλ ϱϮΘΤϳ .4 ϰϟ· 1 Ϧϣ ΔϤϗήϣ ˯΍ήπΧ Ε΍ήϛ ϊΑέ΃ ϰϠϋ B ϕϭΪϨλ ϱϮΘΤϳ ϭ .ΎϤϬϴϤϗέ ϞΠδϧϭ B Ϧϣ ΓΪΣ΍ϭ Γήϛ ΐΤδϧ ϢΛ ˬ A Ϧϣ ΓΪΣ΍ϭ Γήϛ ΐΤδϧ :ΔϴϟΎΘϟ΍ Ι΍ΪΣϷ΍ Ϧϣ Ϟϛ ϝΎϤΘΣ΍ Ϯϫ Ύϣ (1 ."ϦϴϴΟϭί ϦϴϤϗέ ϰϠϋ ϝϮμΤϟ΍" : E ." ϦϴϳΩήϓ ϦϴϤϗέ ϰϠϋ ϝϮμΤϟ΍ " : F " ϲΟϭί ήΧϵ΍ ϭ ϱΩήϓ ΎϤϫΪΣ΃ ϦϴϤϗέ ϰϠϋ ϝϮμΤϟ΍ " : G

:b)L ? k* plblg+2b( plkf)4b( §(?d9 ?d9d !@)2H (

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 01

.ϦϳϭΎϗέί ϦϴΗήϛ ϭ ˯΍ήϤΣ Ε΍ήϛ 4 ϭ ˯΍ήπΧ Ε΍ήϛ 4 ϰϠϋ ϕϭΪϨλ ϱϮΘΤϳ

.ϕϭΪϨμϟ΍ Ϧϣ Ε΍ήϛ 3 ΪΣ΍ϭ ϥ΁ ϲϓ ΐΤδϧ (1 .ΔϨϜϤϤϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ ΐδΣ΃ (΃ ϥϮϠϟ΍ βϔϧ Ϧϣ ΔΑϮΤδϤϟ΍ ΙϼΜϟ΍ Ε΍ήϜϟ΍ ϥϮϜΗ ΚϴΤΑ ΕΎΒΤδϟ΍ ΩΪϋ ΐδΣ΃(Ώ .ϥϮϠϟ΍ ΔϔϠΘΨϣ ΔΑϮΤδϤϟ΍ ΙϼΜϟ΍ Ε΍ήϜϟ΍ ϥϮϜΗ ΚϴΤΑ ΕΎΒΤδϟ΍ ΩΪϋ ΐδΣ΃(Ν ϰϨΜϣ ϰϨΜϣ ϥϮϠϟ΍ ΔϔϠΘΨϣ ΔΑϮΤδϤϟ΍ Ε΍ήϜϟ΍ ϥϮϜΗ ΚϴΤΑ ΕΎΒΤδϟ΍ ΩΪϋ ΐδΣ΃ (Ω .ϝϼΣΈΑ ϭ ϊΑΎΘΘϟΎΑ ϕϭΪϨμϟ΍ Ϧϣ Ε΍ήϛ 3 ΐΤδϧ (2 .ΔϟΎΤϟ΍ ϩάϫ ϲϓ (Ω ϭ (Ν ϭ (Ώ ϭ (΃ ΔϠΌγϷ΍ βϔϧ Ϧϋ ΐΟ΃ .ϝϼΣ· ϥϭΪΑ ϭ ϊΑΎΘΘϟΎΑ ϕϭΪϨμϟ΍ Ϧϣ Ε΍ήϛ 3 ΐΤδϧ (3 .ΔϟΎΤϟ΍ ϩάϫ ϲϓ (Ω ϭ (Ν ϭ (Ώ ϭ (΃ ΔϠΌγϷ΍ βϔϧ Ϧϋ ΐΟ΃

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 02

.΍ήϛΫ 18 ϭ ϰΜϧ΃ 20 : ΍άϴϤϠΗ 38 Ϧϣ Ϣδϗ ϥϮϜΘϳ .ϢδϘϟ΍ ΍άϫ ϲϓ άϴϣϼΗ 4 Ϧϣ ΔϨΠϟ ϦϳϮϜΗ Ϊϳήϧ ˮΎϬϨϳϮϜΗ ϦϜϤϳ ϲΘϟ΍ ϥΎΠϠϟ΍ ΩΪϋ Ϯϫ Ϣϛ (1 ϦϴϣϮϠόϣ άϴϣϼΗ 3 ϥ΃ ΖϤϠϋ ΍Ϋ· ΎϬϨϳϮϜΗ ϦϜϤϳ ϲΘϟ΍ ϥΎΠϠϟ΍ ΩΪϋ Ϯϫ Ϣϛ (2 .ϢϬΤϴηήΗ ϥϮπϓήϳ .ϦϴΗάϴϤϠΗ ϭ ϦϳάϴϤϠΗ ϢπΗ ϲΘϟ΍ ϥΎΠϠϟ΍ ΩΪϋ Ϯϫ Ϣϛ (3 ϦϳάϴϤϠΘϟ΍ ϰϠϋ ϱϮΘΤΗ ϻ ΚϴΤΑ ΎϬϨϳϮϜΗ ϦϜϤϳ ϲΘϟ΍ ϥΎΠϠϟ΍ ΩΪϋ Ϯϫ Ϣϛ (4 ΖϗϮϟ΍ βϔϧ ϲϓ ϦδΣ ϭ ΪϤΣ΃

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 03

.έϮϛΫ 4 ϭ ΙΎϧ· 6 Ϧϣ Γήγ΃ ϥϮϜΘΗ .ΓήγϷ΍ ϩάϫ Ω΍ήϓ΃ ϦϴΑ Ϧϣ Ω΍ήϓ΃ 3 έΎϴΘΧ΍ Ϊϳήϧ .ΎϬϨϳϮϜΗ ϦϜϤϳ ϲΘϟ΍ ΕΎϋϮϤΠϤϟ΍ ΩΪϋ ΩΪΣ (1 .ςϘϓ ΕΎϧϹ΍ ϰϠϋ ϱϮΘΤΗ ϲΘϟ΍ ΕΎϋϮϤΠϤϟ΍ ΩΪϋ ΩΪΣ (2 .ςϘϓ ϦϳήϛΫ ϰϠϋ ϱϮΘΤΗ ϲΘϟ΍ ΕΎϋϮϤΠϤϟ΍ ΩΪϋ ΩΪΣ (3 .ϞϗϷ΍ ϰϠϋ ήϛΫ ϰϠϋ ϱϮΘΤΗ ϲΘϟ΍ ΕΎϋϮϤΠϤϟ΍ ΩΪϋ ΩΪΣ (4

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 04 ϱϮΘΤϳ ϭ .˯΍ήπΧ Ε΍ήϛ 3 ϭ ˯΍ήϤΣ Ε΍ήϛ 4 ϰϠϋ U 1 ϕϭΪϨλ ϱϮΘΤϳ .˯΍ήϔλ Γήϛ ϭ ˯΍ήπΧ Ε΍ήϛ 2 ϭ ˯΍ήϤΣ Ε΍ήϛ 5 ϰϠϋ U 2 ϕϭΪϨλ Ϧϣ Γήϛ ϭ U 1 ϕϭΪϨμϟ΍ Ϧϣ ϦϴΗήϛ ΪΣ΍ϭ ϥ΁ ϲϓ ϭ Ύϴ΋΍Ϯθϋ ΐΤδϧ ..U 2 ϕϭΪϨμϟ΍ ˮΕ΍ήϛ ΙϼΛ ΐΤδϟ ΕΎϴϧΎϜϣϹ΍ ΩΪΣ Ϯϫ Ύϣ (1 :ΔϴϟΎΘϟ΍ ΕϻΎΤϟ΍ Ϧϣ Ϟϛ ϲϓ ΕΎϴϧΎϜϣϹ΍ ΩΪϋ ΩΪΣ (2 .˯΍ήϤΣ Ε΍ήϛ ΙϼΛ ΐΤγ -΃ .ςϘϓ ΓΪΣ΍ϭ ˯΍ήπΧ Γήϛ ΐΤγ -Ώ .˯΍ήϔλ Γήϛ ϭ Ϧϳϭ΍ήπΧ ϦϴΗήϛ ΐΤγ -Ν .ϥϮϟ Ϟϛ Ϧϣ Γήϛ ΐΤγ -Ω

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 05

.˯΍ήϤΣ Ε΍ήϛ 3 ϭ ˯΍ήπΧ Ε΍ήϛ 5 ϰϠϋ ϕϭΪϨλ ϱϮΘΤϳ .ϝϼΣ· ϥϭΪΑ ϭ ϊΑΎΘΘϟΎΑ Ε΍ήϛ 4 ϕϭΪϨμϟ΍ Ϧϣ ΐΤδϧ .ΔϨϜϤϤϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ ΩΪΣ (1 .˯΍ήϤΣ ϰϟϭϷ΍ ΙϼΜϟ΍ Ε΍ήϜϟ΍ ΎϬϴϓ ϥϮϜΗ ϲΘϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ ΩΪΣ (2 .˯΍ήϤΣ ϰϟϭϷ΍ ΓήϜϟ΍ ΎϬϴϓ ϥϮϜΗ ϲΘϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ ΩΪΣ (3 .˯΍ήϤΣ ΓΪΣ΍ϭ Γήϛ ϰϠϋ ϱϮΘΤΗ ϲΘϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ ΩΪΣ (4 .ςϘϓ ϦϴΗϭ΍ήπΧ ϦϴΗήϛ ϢπΗ ϲΘϟ΍ ΕΎΒΤδϟ΍ ΩΪϋ ΩΪΣ (5

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 06

ϞϤΤΗ Ε΍ήϛ ΙϼΛ ϰϠϋ ϭ ˬ 0 Ϣϗήϟ΍ ϥϼϤΤΗ ϦϴΗήϛ ϰϠϋ ϕϭΪϨλ ϱϮΘΤϳ .2 Ϣϗήϟ΍ ϞϤΤΗ Ε΍ήϛ ϊΑέ΃ ϰϠϋ ϭ ˬ 1 Ϣϗήϟ΍ .ϕϭΪϨμϟ΍ Ϧϣ Ε΍ήϛ 3 ϝϼΣΈΑ ϭ ϊΑΎΘΘϟΎΑ ΐΤδϧ

ϦϴϤϗήϟ΍ ωϮϤΠϤΑ ΔΒΤγ Ϟϛ ςΑήϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ X ϦϜϴϟ (2 .ΎϤϬϴϠϋ ϞμΤϤϟ΍ . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ϝΎϤΘΣ΍ ϥϮϧΎϗ ςϋ΃ (΃ . E X ϲοΎϳήϟ΍ ϞϣϷ΍ ΐδΣ΃ (Ώ ϰϟ· Γήϛ Ϟϛ Ϊϴόϧ Γήϣ Ϟϛ ϲϓ ϭ Ε΍ήϣ βϤΧ [ έΎΒΘΧϻ΍ έήϜϧ (3 .ϪϨϣ ΖΒΤγ ϱάϟ΍ ϕϭΪϨμϟ΍ ϲΘϔϠΘΨϣ ϦϴΗήϛ ϰϠϋ ςΒπϟΎΑ Ε΍ήϣ ΙϼΛ ϝϮμΤϟ΍ ϝΎϤΘΣ΍ Ϯϫ Ύϣ ˮϥϮϠϟ΍

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 15

:ϕΩΎϴΑ 8 ϰϠϋ βϴϛ ϱϮΘΤϳ .ϞϜθϟ΍ ΚϠΜϣ ϭ ήϤΣ΃ ϪϧϮϟ ΪΣ΍ϭ .ϞϜθϟ΍ ΎΜϠΜϣ ϭ ήπΧ΃ ΎϤϬϧϮϟ ϥΎϨΛ΍ .ϞϜθϟ΍ ϮϠϴτΘδϣ ϭ ήϤΣ΃ ϢϬϧϮϟ 5 ϊϴϤΟ ϥ΃ νήΘϔϧ ϭ βϴϜϟ΍ Ϧϣ ϦϴϗΪϴΑ ΪΣ΍ϭ ϥ΁ ϲϓ ϭ Ύϴ΋΍Ϯθϋ ΐΤδϧ :ϲϟΎΘϟΎϛ B ϭ A ϦϴΗΪΤϟ΍ ήΒΘόϧ ϭ .ϝΎϤΘΣϻ΍ ΔϳϭΎδΘϣ ΕΎΒΤδϟ΍ ." Ϣϗήϟ΍ ϲΘϔϠΘΨϣ ϦϴΗήϛ ϰϠϋ ϝϮμΤϟ΍ " : A ." ϥϮϠϟ΍ ϲΘϔϠΘΨϣ ϦϴΗήϛ ϰϠϋ ϝϮμΤϟ΍ " : B . A B ϭ B ϭ A ΔϴϟΎΘϟ΍ Ι΍ΪΣϷ΍ ϝΎϤΘΣ΍ ΐδΣ΃ (1 ˮϥϼϘΘδϣ B ϭ A ϥΎΛΪΤϟ΍ Ϟϫ (2 ϝΎϤΘΣϹ΍ Ϯϫ Ύϣ .ϥϮϠϟ΍ βϔϧ Ϧϣ ϦϴΘϗΪϴΑ ϰϠϋ ΎϨϠμΣ ˬ ΐΤγ ΔϴϠϤϋ ΪόΑ (3 ˮϞϜθϟ΍ βϔϧ Ϧϣ ΎϧϮϜϳ ϥ΃

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 16

ϥ΁ ϲϓ ϭ Ύϴ΋΍Ϯθϋ ΐΤδϧ .4 ϰϟ· 1 Ϧϣ ΔϤϗήϣ Ε΍ήϛ 4 ϰϠϋ ϕϭΪϨλ ϱϮΘΤϳ ϝΎϤΘΣ΍ βϘϧ ΎϬϟ ϊΑέϷ΍ Ε΍ήϜϟ΍ ϥ΃ νήΘϔϧ .ϕϭΪϨμϟ΍ Ϧϣ ϦϴΗήϛ ΪΣ΍ϭ .ΐΤδϟ΍ .ΕΎϴϧΎϜϣϷ΍ ϥϮϛ ΩΪΣ (1 ΩΪόϟΎΑ ^a, b ` ΔϴϧΎϜϣ· Ϟϛ ςΑήϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ X ϦϜϴϟ (2 .ϦϴΘΑϮΤδϤϟ΍ ϦϴΗήϜϟ΍ ΎϤϗέ ΎϤϫ b ϭ a ΚϴΣ 1 ϲϘϴϘΤϟ΍ . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ϝΎϤΘΣ΍ ϥϮϧΎϗ ΩΪΣ ΩΪόϟΎΑ ^a, b ` ΔϴϧΎϜϣ· Ϟϛ ςΑήϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ Y ϦϜϴϟ (3 a b

ϦϴΗήϜϟ΍ ΎϤϗέ ΎϤϫ b ϭ a ΚϴΣ 1 1 ϲϘϴϘΤϟ΍ a

. X

. X ,Y ΝϭΰϠϟ ΐΣΎμϤϟ΍ ϥϮϧΎϘϟ΍ ΩΪΣ .ϦϴΘΑϮΤδϤϟ΍

1 ΙΪΤϟ΍ ϝΎϤΘΣ΍ ΐδΣ΃ ϖϘΤϣ Y z 0 ΙΪΤϟ΍ ϥ΃ ΎϤϠϋ (4

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 17

:ϲϠϳ ΎϤϛ ϑήόϤϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ X ϦϜϴϟ (2 .ϦϴϴΟϭί ϦϴΘΑϮΤδϤϟ΍ ϦϴΗήϜϟ΍ ΎϤϗέ ϥΎϛ ΍Ϋ· ˯΍ήϤΤϟ΍ ΓήϜϟ΍ Ϣϗέ ϱϭΎδϳ X .ϦϴϳΩήϓ ϦϴΘΑϮΤδϤϟ΍ ϦϴΗήϜϟ΍ ΎϤϗέ ϥΎϛ ΍Ϋ· ˯΍ήπΨϟ΍ ΓήϜϟ΍ Ϣϗέ ϱϭΎδϳ X ΎϴΟϭί ΎϤϫΪΣ΃ ϥΎϛ ΍Ϋ· ϦϴΘΑϮΤδϤϟ΍ ϦϴΗήϜϟ΍ ϲϤϗέ ήΒϛ΃ ϱϭΎδϳ X .ΎϳΩήϓ ήΧϵ΍ ϭ . X ΎϫάΧ΄ϳ ϲΘϟ΍ ϢϴϘϟ΍ ΩΪΣ (΃ . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ ϝΎϤΘΣ΍ ϥϮϧΎϗ ΩΪΣ (Ώ

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 12

ϑΪϬϟ΍ ϪΘΑΎλ· ϝΎϤΘΣ΍ .ιΎλήϟ΍ Ϧϣ ϦϴϋϮϧ ϼϤόΘδϣ ΎΘΑΎΛ ΎϓΪϫ ΪϤΣ΃ ϲϣήϳ 8 Ϧϣ ΔλΎλήΑ ϑΪϬϟ΍ ϪΘΑΎλ· ϝΎϤΘΣ΍ ϭ Ϯϫ A ωϮϨϟ΍ Ϧϣ ΔλΎλήΑ 10 6 . Ϯϫ B ωϮϨϟ΍ 10 ϪΗΎΑΎλ· ΩΪϋ X ϦϜϴϟ . A ωϮϨϟ΍ Ϧϣ ϦϴΘλΎλήΑ ϑΪϬϟ΍ ΪϤΣ΃ ϲϣήϳ (1 .ϑΪϬϟ΍ . E X ϲοΎϳήϟ΍ ϞϣϷ΍ ΐδΣ΃ ϭ . X ϥϮϧΎϗ ςϋ΃ .B ωϮϨϟ΍ Ϧϣ ΔλΎλήΑ ϢΛ A ωϮϨϟ΍ Ϧϣ ΔλΎλήΑ ϑΪϬϟ΍ ΪϤΣ΃ ϲϣήϳ (2 .Ύόϣ ϦϴΘλΎλήϟΎΑ ϑΪϬϟ΍ ϪΘΑΎλ· ϝΎϤΘΣ΍ ΐδΣ΃ (΃ .ϞϗϷ΍ ϰϠϋ ϦϴΘλΎλήϟ΍ ϯΪΣΈΑ ϑΪϬϟ΍ ϪΘΑΎλ· ϝΎϤΘΣ΍ ΐδΣ΃ (Ώ Ϧϣ ΕΎλΎλέ 3 ϰϠϋ ϱϮΘΤϳ βϴϛ Ϧϣ ϦϴΘλΎλέ Ύϴϧ΂Η ΪϤΣ΃ ΐΤδϳ (3 .B ωϮϨϟ΍ Ϧϣ 4 ϭ A ωϮϨϟ΍ .A ωϮϨϟ΍ Ϧϣ ϦϴΘλΎλέ ΐΤγ ϝΎϤΘΣ΍ ΐδΣ΃ (΃ .ωϮϨϟ΍ ϲΘϔϠΘΨϣ ϦϴΘλΎλέ ΐΤγ ϝΎϤΘΣ΍ ΐδΣ΃ (Ώ 328 :Ϯϫ ϦϴΗήϣ ϑΪϬϟ΍ ΪϤΣ΃ ΔΑΎλ· ϝΎϤΘΣ΍ ϥ΃ ΖΒΛ΃ (Ν . 700

˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 13 ϭ ˯΍ΩϮγ Ε΍ήϛ 3 ϭ ˯ΎπϴΑ Ε΍ήϛ 4 :Ε΍ήϛ 9 ϰϠϋ U 1 ϕϭΪϨλ ϱϮΘΤϳ .ήϤΣ΃ ΎϤϬϧϮϟ ϥΎΗήϛ ϦϜϴϟ ϭ .U 1 ϕϭΪϨμϟ΍ Ϧϣ Ε΍ήϛ 3 ΪΣ΍ϭ ϥ΁ ϲϓ ϭ Ύϴ΋΍Ϯθϋ ΐΤδϧ (1 n ΚϴΣ 2n 4 ΩΪόϟΎΑ ΔΒΤγ Ϟϛ ςΑήϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ X .ΔΑϮΤδϤϟ΍ ˯ΎπϴΒϟ΍ Ε΍ήϜϟ΍ ΩΪϋ Ϯϫ . X ϝΎϤΘΣ΍ ϥϮϧΎϗ ςϋ΃ (΃ . X ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϠϟ ϲοΎϳήϟ΍ ϞϣϷ΍ ΐδΣ΃ (Ώ ˯ΎπϴΑ Ε΍ήϛ 7 :Ε΍ήϛ 10 ϰϠϋ ϱϮΘΤϳ U 2 ήΧ΁ ΎϗϭΪϨλ ήΒΘόϧ (2 .˯΍ΩϮγ Ε΍ήϛ 3 ϭ U 2 ϕϭΪϨμϟ΍ Ϧϣ ΓΪΣ΍ϭ Γήϛ Ύϴ΋΍Ϯθϋ ΐΤδϧ :ϲϟΎΘϟ΍ έΎΒΘΧϻΎΑ ϡϮϘϧ

ΙϼΛ ϭ 2 Ϣϗήϟ΍ ϥϼϤΤΗ ϦϴΗήϛ ϭ 1 Ϣϗήϟ΍ ϞϤΤΗ Γήϛ ϰϠϋ βϴϛ ϱϮΘΤϳ Ϧϣ ΓΪΣ΍ϭ Γήϛ ΐΤδϧ ϢΛ ΎϬϧϮϟ ϞϴΠδΗ ΪόΑ U 1 ϕϭΪϨμϟ΍ ϲϓ ΎϬόπϧ ϭ .3 Ϣϗήϟ΍ ϞϤΤΗ Ε΍ήϛ .U 1 ϕϭΪϨμϟ΍ ΎΒϨΟ ΔΑϮΤδϤϟ΍ Ε΍ήϜϟ΍ ϡΎϗέ΃ ϞΠδϧ ϭ Ε΍ήϛ ΙϼΛ ϝϼΣΈΑ ϭ ϊΑΎΘΘϟΎΑ ΐΤδϧ :ϦϴϴϟΎΘϟ΍ ϦϴΗΪΤϟ΍ Ϧϣ Ϟϛ ϝΎϤΘΣ΍ ΐδΣ΃ ΩΪϋ ϰϠϋ ϞμΤϧ ΚϴΤΑ ΐΤδϟ΍ ΐϴΗήΗ ϲϓ ϦϴϤϴϟ΍ ϰϟ· έΎδϴϟ΍ Ϧϣ ΐϨΟ ϰϟ· ."˯΍ήϤΣ έΎΒΘΧϻ΍ ήΧ΁ ϲϓ ΔΑϮΤδϤϟ΍ ΓήϜϟ΍" : E 1 .ϝΎϤΘΣϹ΍ ΔϳϭΎδΘϣ ΕΎΒΤδϟ΍ ϊϴϤΟ ϥ΃ ήΒΘόϧ .ϡΎϗέ΃ ΙϼΛ Ϧϣ ϥϮϜϣ ." ˯ΎπϴΑ έΎΒΘΧϻ΍ ήΧ΁ ϲϓ ΔΑϮΤδϤϟ΍ ΓήϜϟ΍ " : E 2 .ΔϳΩήϓ ϡΎϗέ΃ ΔΛϼΛ Ϧϣ ϥϮϜϣ ΩΪϋ ϰϠϋ ϝϮμΤϟ΍ ϝΎϤΘΣ΍ ΐδΣ΃ -΃ (1 .ϲΟϭί ΩΪϋ ϰϠϋ ϝϮμΤϟ΍ ϝΎϤΘΣ΍ ΐδΣ΃ -Ώ ˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰˰ 14 ϲΘϟ΍ ΔϴΟϭΰϟ΍ ϡΎϗέϷ΍ ΩΪϋ ϱϭΎδϳ ϱάϟ΍ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ X ϦϜϴϟ (2 ϞϤΤΗ ˯΍ΩϮγ Ε΍ήϛ 3 ϰϠϋ U 1 ϱϮΘΤϳ :ΚϴΤΑ U 2 ϭ U 1 ϦϴϗϭΪϨλ ήΒΘόϧ ϲ΋΍Ϯθόϟ΍ ήϴϐΘϤϟ΍ Y ϦϜϴϟ ϭ ˬϪϴϠϋ ϞμΤϤϟ΍ ΩΪόϟ΍ ΔΑΎΘϛ ΎϬϴϠϋ ϞϤΘθΗ 1 ϱϭΎδϳ ϱάϟ΍ ϭ ΎϴΟϭί ΍ΩΪϋ ϞμΤϤϟ΍ ΩΪόϟ΍ ϥΎϛ ΍Ϋ· 0 ϱϭΎδϳ ϱάϟ΍ Ε΍ήϛ 4 ϰϠϋ U 2 ϱϮΘΤϳ ϭ . 2 Ϣϗήϟ΍ ϥϼϤΤΗ ϦϳϭΎπϴΑ ϦϴΗήϛ ϭ 1 Ϣϗήϟ΍ .ΎϳΩήϓ ΍ΩΪϋ ϞμΤϤϟ΍ ΩΪόϟ΍ ϥΎϛ ΍Ϋ· Γήϛ ΐΤδϧ" : [ έΎΒΘΧϻ΍ ήΒΘόϧ . 2 ˬ 2 ˬ 1 ˬ 1 :ϡΎϗέϷ΍ ϞϤΤΗ ˯΍ΩϮγ . X ,Y ΝϭΰϠϟ ΐΣΎμϤϟ΍ ϥϮϧΎϘϟ΍ ςϋ΃ -΃ ." U 2 Ϧϣ Γήϛ ϭ U 1 Ϧϣ .ϦϴϴθϣΎϬϟ΍ ϦϴϧϮϧΎϘϟ΍ ΩΪΣ -Ώ :ϦϴϴϟΎΘϟ΍ ϦϴΗΪΤϟ΍ Ϧϣ Ϟϛ ϝΎϤΘΣ΍ ΐδΣ΃ (1 .ϚΑ΍ϮΟ ϞϠϋ ˮϥϼϘΘδϣ Y ϭ X ϥ΍ήϴϐΘϤϟ΍ Ϟϫ -Ν ." Ϣϗήϟ΍ ϲΘϔϠΘΨϣ ϦϴΗήϛ ϰϠϋ ϝϮμΤϟ΍ " : A ." ϥϮϠϟ΍ ϲΘϔϠΘΨϣ ϦϴΗήϛ ϰϠϋ ϝϮμΤϟ΍ " : B