ΠΛΗ20 ΜΑΘΗΜΑ 0.1

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ΠΛΗ20 ΜΑΘΗΜΑ 0.1

Transcript of ΠΛΗ20 ΜΑΘΗΜΑ 0.1

  • 20 0:

    0.1:

  • .

    .

    1.

    2 , 20, 0.1:

    1.

    2.

    3. 1.

    2.

    4.

    5.

    1.

    2.

    3.

    4.

    5.

    6.

    .

  • .

    3 , 20, 0.1:

    (-)

    (-) (-)

  • . 1.

    4 , 20, 0.1:

    :

    :

    1 9

    .

    },,,,,,{ =

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

    .

    :

    . ..

    :

    , | :

    }20,18,16,14,12,10{=

    }2010|{ = xxx

  • . 2. . :

    :

    5 , 20, 0.1:

    ( 0) :

    :

    R

    , : {}=

  • . 2.

    :

    5

    6 , 20, 0.1:

    N5 5

    4.4

    ( )

    N5

    N4.4

    }3,2,1{=A}2,1,3{=B

    ( )

    ,

    .

    == ( )

    }2,1,3{=B

    }3,3,2,2,2,1,1{=

  • . 2. .

    .

    :

    7 , 20, 0.1:

    :

    :

    :

    :

    ,...}13,11,7,5,3,2{=A

    },,,{ patjimjohntom=

    }1)(,1)(,)({ 4 32 ++=+=== xxxhxxgxxf !

    :

    }1)(,1)(,)({ ++=+=== xxxhxxgxxf

    },},5,2{},3,2,1{{ =

    }}5,1{,7,5,,2,14.3,{ tom=

  • . 3. 1. :

    8 , 20, 0.1:

    ( ) BA

    :

    :

    :

    :

    :

    :

    ( )

    BA

    },,,{},,{ dcbacba N}3,5,1{

    }3,2,1{}3,2,1{ }3,2,1{}4,3,2,1{

    }3,1{}2,1{ :

    :

    :

    }3,1{}2,1{

    BxAxBA

    ABBABA =

  • . 3. 2. :

    9 , 20, 0.1:

    ( ) BA

    :

    :

    :

    :

    :

    :

    ( ) , .

    BA

    },,,{},,{ dcbacba N}3,5,1{

    }3,2,1{}3,2,1{ }3,2,1{}4,3,2,1{

    }3,1{}2,1{ :

    :

    }3,1{}2,1{

    xxBABA

  • . 4. ,

    ..

    10 , 20, 0.1:

    = 4 .

    || ( ). :

    ,

    .

    },,,{ patjimjohntom=

    4|| =

    , ..

    N,Z,Q,R :

    |||| BABA |||| BABA

  • . 5. .

    :

    11 , 20, 0.1:

    BA

    BA

    BA

    BA

    :

    :

    AxB)(AP

  • . 5. 1. :

    12 , 20, 0.1:

    :

    Venn, :

    :

    }|{ BxAxxBA =

    A B

    ={0,1,2,3} ={2,3,4,5} }5,4,3,2,1,0{= BA

  • :

    . 5. 2.

    13 , 20, 0.1:

    :

    Venn, :

    :

    }|{ BxAxxBA =

    A B

    ={0,1,2,3} ={2,3,4,5} }3,2{= BA

  • . 5. 2. :

    ,

    14 , 20, 0.1:

    ,

    .

    . :

    ,

    BA 0|| BA

    A B

    ,

    . : = BA 0|| = BA

    A B :

  • . 5. 2. ( )

    .

    15 , 20, 0.1:

    .

    :

    :

    |||||||| BABABA +=

    |||||||| CBACBA ++=

    ||||||||

    ||||||||

    CBACBCABA

    CBACBA

    +

    ++=

  • . 5. 3. :

    16 , 20, 0.1:

    :

    Venn, :

    :

    }|{ AxxA =

    AU

    ={0,1,2,3} U={0,1,2,3,4,5,6} }6,5,4{=A

  • :

    . 5. 4.

    17 , 20, 0.1:

    :

    Venn, :

    :

    }|{\ BxAxxBABA ==

    A B

    ={0,1,2,3} ={2,3,4,5} }1,0{= BA {4,5}B A =

  • . 5. 5. :

    18 , 20, 0.1:

    :

    (x,y) x y, (

    )

    :

    }|),{( ByAxyxAxB =

    ) ={1,2} ={a,b,c} :

    :)}2,(),1,(),2,(),1,(),2,(),1,{(

    )},2(),,2(),,2(),,1(),,1(),,1{(ccbbaaBxA

    cbacbaAxB=

    =

    ||*|||||| BABxAAxB ==

  • . 5. 6. :

    19 , 20, 0.1:

    ( 2 P(A) ) :

    ={1,2} :

    ={1,2,3} :

    ( 2 P(A) ) :

    }|{)( = pi xxAP

    }}2,1{},2{},1{,{)( =AP ={1,2,3} :

    :

    }}3,2,1{},3,2{},3,1{},2,1{},3{},2{},1{,{)( =AP

    ||2|)(| =AP

  • .

    1

    :

    20 , 20, 0.1:

    .6}2,1{.5

    }2,1{}2,1{.4}2,1{}2,1{.3}2,1{}2,1{.2

    5.1

    RQZNRQZN

    .9

    .8}{.7

    .6

  • .

    2 Venn :

    21 , 20, 0.1:

    .1 BA

    )(\)(.4)()(.3

    )(.2.1

    BABAABBA

    CBABA

  • .

    3 :

    22 , 20, 0.1:

    }4,3,2,1{.1 =A}}2,1{,1,{.2

    }4,3,2,1{.1=

    =

    BA

  • .

    4 150 50 , 80 , 40

    23 , 20, 0.1:

    , 40 .

    .