2. Бақылау жұмысы. Логикалық функциялардың толық жүйелері. Комбинаторика.
а) f1 және f2 функцияларының қандай класқа жататындығын анықтаңыз. Пост теоремасына сүйенiп
{ f1 ,f2 } функциялар жүйесiнiң толықтығын тексерiңiз.
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п/п
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Тапсырмалар варианттары
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п/п
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Тапсырмалар варианттары
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1
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F1=(0 1 0 1 1 0 1 1)
f2=(x V y)(z x)
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8
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f1=(0 1 1 0 1 1 1 0)
f2=x y V z
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15
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f1=(0 1 1 1 1 1 0 1)
f2=(x V y) xyz
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2
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F1=(0 1 0 1 1 0 0 1)
f2=(x y) V
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9
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f1=(0 1 1 0 0 0 1 1)
f2=(x y)(y V x)
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16
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f1=(1 0 0 1 0 1 0 0)
f2=(x V y)(z x)
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3
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f1=(0 1 0 1 0 1 1 0)
f2=x ( V z)
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10
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f1=(0 1 1 0 1 1 0 1)
f2=(x z)(xVy)
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17
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f1=(1 0 0 1 1 0 0 1)
f2=(x y) z
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4
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f1=(0 1 0 1 0 0 1 1)
f2=(x ) z
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11
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f1=(0 1 1 1 0 1 0 0)
f2=xy zx
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18
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f1=(1 0 0 1 0 1 1 0)
f2=x V yz
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5
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F1=(0 1 0 1 1 1 0 1)
f2=x y V z (x )
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12
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f1=(0 1 1 1 1 0 0 1)
f2= yz(z V x)
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19
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f1=(1 0 0 1 0 0 1 1)
f2=(x y) z
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6
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f1=(0 1 1 0 0 1 0 0)
f2=x y (y z)
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13
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f1=(0 1 1 1 0 1 1 0)
f2=(x y) (z y)
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20
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f1=(1 0 0 1 1 1 0 1)
f2=xy V z(x y)
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7
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f1=(0 1 1 0 1 0 0 1)
f2=![](data:image/png;base64,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) V(x y z)
|
14
|
f1=(0 1 1 1 0 0 1 1)
f2=(x V y) (z V y)
|
21
|
f1=(0 1 0 1 0 1 1 0)
f2=x ( V z)
|
б) Берiлген А цифрлар жиынын пайдаланып қанша әртүрлi үш таңбалы натурал сан алуға болады, егер 1) Әр цифр бiрден артық пайдаланылмайды;
2) Бiр цифрды бiрнеше рет пайдалануға болады;
б) Тапсырма варианттары
1. А={3,4,5,6}
|
5. А={2,3,5,7,9}
|
9. А={2,5,7,8,9}
|
13. А={3,4,7,9}
|
17. А={2,4,7}
|
2. А={1,3,5,7}
|
6. А={1,4,8,9}
|
10. А={3,4,7,8,9}
|
14. А={2,5,7,8}
|
18. А={1,3,5,8,9}
|
3. А={2,5,6,7,8}
|
7. А={2,3,4,5}
|
11. А={1,2,5,6}
|
15. А={1,3,4}
|
19. А={3,4,7,9}
|
4. А={3,4,5,9}
|
8. А={3,7,8,9}
|
12. А={2,3,4,5,6}
|
16. А={3,5,7,8,9}
|
20. А={2,5,6,7,8}
|
в) Тапсырма варианттары
5 кiтапты сөреге қанша әдiспен орналастыруға болады
Серванттың бiр қатарына 6 бокалды қанша әдiспен орналастыруға болады.
Столға 8 адамнан тұратын президиумды қанша әдiспен отырғызуға болады?
7 адамды қанша әдiспен сапқа тұрғызуға болады?
Класқа 10 партаны қанша әдiспен қоюға болады?
А,Б,В,Г,Д әрiптерiнен тұратын тiзбектi қанша әдiспен құруға болады?
«Персик» сөзiнен қанша әртүрлi 6 әрiптiк тiзбектер алуға болады?
5 пәннен тұратын оқу кестесiн бiр күнге неше тәсiлмен құруға болады?
Дастарханға 4 адамды қанша әдiспен отырғызуға болады?
Әртүрлi 7 карточка салынған қорапты қанша әдiспен араластыруға болады?
Ұсынылған 6 пәннен 3 пәндi неше әдiспен таңдауға болады?
Қолда бар 7 түрлi жемiстiң екеуiн қанша әдiспен таңдауға болады?
10 адамнан жиналысқа баратын 3 адамды қанша әдiспен таңдауға болады?
Конкурсқа 7 притенденттен 4 студенттi қанша әдiспен таңдауға болады?
Сөреде тұрған 10 кiтаптан неше әдiспен оқуға 3 кiтап таңдауға болады?
10 фильмнен тұратын видеотекадан неше әдiспен әртүрлi 4 фильм таңдауға болады?
Шкафта iлулi тұрған 8 галстуктен неше әдiспен әртүрлi 2 галстук таңдауға болады?
Сатылымдағы 9 түрлi газеттен неше әдiспен әртүрлi 5 газет сатып алуға болады?
8 адамнан тұратын топтан неше әдiспен программалау курсына 3 адам таңдауға болады?
Менюде бар 7 тағамнан неше әдiспен 3 түрлi тағам таңдауға болады?
Тапсырмалар варианттары
Темiр жол бекетiнде m бағдаршам бар. Егер бағдаршам «қызыл», «жасыл», «сары» 3 күйде болса, олардан неше түрлi сигналдардың комбинациясын беруге болады?
Бiр мемлекетте тiстерiнiң жиынтығы бiрдей 2 тұрғын болмаптыегер адамның тiстерiнiң саны 32 десек бұл мемлекеттiң тұрғындарының ең көп саны қанша болуы мүмкiн?
Қайталап пайдалануға болатын тақ цифрлардан неше түрлi 4 таңбалы сан құрастыруға болады?
Әртүрлi 12 оқу құралын 4 студентке неше әдiспен бәлiп беруге болады?
9 түрлi күмiс ақшаны 2 қалтаға неше түрлi әдiспен салуға болады?
Үшеуi ток импульсi , екеуi үзiлiсте болатын әрiптегi 5 түрлi сигналдан алфавиттiң неше әрiбiн құрауға болады?
«Статистика», «Парабола» сөздерiндегi әртүрлi алмастырулардың санын анықтаңыз.
Апада 2 алма, 3 алмұрт және 4 апельсин бар. Олардан 9 күн бойы баласына бiр талдан берiп отырады. Қанша әдiспен берiп отыруға болады?
Почта бөлiмшесiнде 9 түрлi ашық хат сатылады. Ашық хаттың әр түрiнiң саны 8ден кем болмаса 8 ашық хаттан тұратын жиынтықты неше әдiспен сатып алуға болады?
3 жiгiт пен 2 қыз жұмыс орнын iздейдi. Егер қалада 3 тек жiгiттер дi қабылдайтын құю цехтары бар 3 зауыт, қыздарды қабылдайтын 2 тоқыма фабрикасы және жiгiттердi де, қыздарды да қабылдайтын 2 фабрика болса неше әдiспен жұмыс таңдауға болады?
Бес қызметкерден тұратын топқа 3жолдама бөлiндi. Жолдамалар әртүрлi болса, оны неше әдiспен үлестiруге болады?
Взводта 3 сержант және 30солдат бар. Қарауылға 1 сержант пен 3 солдатты неше әдiспен жiберуге болады?
Неше әдiспен 15 студенттi 3 оқу тобына бесеуден бөлуге болады?
Жарысқа қатысушы 17 спортшыға бiрiншi, екiншi және үшiншi орындарды неше әдiспен бөлудiң мүмкiндiгi бар?
5әйел және 7 ер адамнан тұратын қазылар алқасы 8 әйел және 11 ер адамнан тұратын тiзiмнен таңдалуы тиiс. Құрамы неше түрлi қазылар алқасын таңдауға болады?
Раушангүлiнiң 4 сорты сатылады. Қанша әртүрлi букет құруға болады?
Бiрдей 20шарды. Әртүрлi 4 урнаға неше әдiспен салуға болады?
Әртүрлi 10 шарды, 3 урнаға қанша әдiспен орналастыруға болады?
Белгiлi әртүрлi 7 аттан 4 күшiкке неше әдiспен ат беруге болады?
25 адамнан тұратын топты 7 коалицияға неше әдiспен бөлуге болады:5адамнан 2 коалиция, 7 адамнан 1 коалиция, 2 адамнан 4 коалиция;
д)Жиындарды бөлiктеу. n объектен тұратын жиынды m бос емес бөлiктерге бөлуге болады?
Тапсырма варианттары:
1. n =7, m =3
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5. n =7, m =4
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9. n =7, m =2
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13. n =5, m =4
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17. n =5, m =3
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2. n =4, m =2
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6. n =7, m =4
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10. n =8, m =3
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14. n =6, m =2
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18. n =5, m =3
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3. n =8, m =6
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7. n =8, m =2
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11. n =5, m =3
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15. n =5, m =2
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19. n =5, m =3
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4. n =7, m =5
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8. n =4, m =3
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12. n =6, m =4
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16. n =6, m =3
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20. n =6, m =5
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3-Бақылау жұмысы. Ең кіші қосылу туралы есеп.
7 төбелі бағытталмаған толық графтың қабырғалар салмағының матрицасы берілген. Оң ең кіші
қаңқалы ағашын табыңыз. Жеткілікті түсініктемелермен оны графикалық түрде кескіндеңіз.
Тапсырма варианттары.
1.
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∞
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4-Бақылау жұмысы. Ең қысқа жол туралы есеп.
Байланысты тиелген бағытталмаған графта қабырғаларының салмағы L=(l1 ,l2...,l13) түрінде берілген. V0 мен V7 төбелерінің арасындағы ең қысқа жолды табыңыз.
Тапсырмалар варианттары.
1. L = ( 3, 7, 12, 8, 24, 9, 13, 5, 4, 2, 16, 3, 6 )
2. L = ( 5, 41, 23, 1, 7, 27, 42, 92, 6, 9, 33, 55,4 )
3. L = ( 51, 4, 52, 9, 5, 2, 11, 3, 42, 6, 9, 22, 8)
4. L = ( 5, 41, 2, 49, 25, 2, 1, 3, 39, 7, 10, 21, 3)
5. L = ( 7, 3, 2, 19, 7, 12, 52, 7, 2, 9, 9, 31, 12)
6. L = ( 27, 14, 35, 71, 4, 1, 1, 13, 21, 16,49, 4, 8)
7. L = ( 6, 32, 12, 4, 5, 2, 11, 3, 42, 6, 9, 22, 3)
8. L = ( 41, 5, 2, 19, 35, 14, 1, 23, 12, 3, 8, 72, 3)
9. L = ( 72, 35, 2, 3, 6, 13, 41, 4, 21, 21, 6, 5, 7)
10. L = ( 1, 7, 5, 1, 8, 4, 7, 12, 4, 8, 6, 24, 3)
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1
11. L = ( 1, 44, 35, 21, 61, 1, 31, 2, 4, 1, 5, 32, 82)
12. L = ( 7, 32, 2, 31, 9, 2, 17, 9, 3, 56,19, 2, 17)
13. L = ( 6, 23, 32, 6, 9, 12, 41, 5, 24, 6, 8, 6, 9)
14. L = ( 5, 24, 2, 5, 9, 1, 61, 53,22, 3, 1, 61, 2)
15. L = (6, 34, 21, 81, 2, 7, 31, 6, 19, 4, 2, 2, 1)
16. L = ( 20, 5, 2,19, 31, 7, 19, 4, 2, 8, 3, 2, 5)
17. L = ( 8, 16, 47, 2, 61, 6, 21, 7, 2, 42, 45, 2, 4)
18. L = ( 6, 32, 81, 4, 6, 21, 41, 74, 58, 3, 1, 20, 7)
19. L = ( 10, 5, 12, 7, 93, 1, 10, 4, 6, 34, 8, 13, 6)
20. L = ( 1, 34, 2, 19, 6, 42, 37, 25, 2, 26, 91, 52,
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2.6.2.Семестрлiк жұмыстардың тақырыптары мен варианттары
(8 семестрлiк жұмыс )
1 семестрлiк жұмыс.Жиындармен операциялар, Декарт көбейтiндiсiн , оның геометриялық мағынасы.
а) А,В жиындары берiлген. АUB,А∩B,A\B,B\A,AХB,AХB табыңыз. Декарт көбейтiнiдiсiнiң геометрия лық мағына берiңiз.
Тапсырма варианттары.
1. А={2 , 3} , B={3,4,5}
2. А={x | 2x 3} , B={y | 3 y 5}
3. А={1,2 , 3} , B={x|2x5}
4. А={2 , 3 , 4} , B={3 ,4 }
5. А={y|1y 3} , B={x|2x5}
6. А={2 , 5} , B={7,9,2}
7. А={2 , 3 , 4} , B={3 ,4,7 }
8. А={y|2y 4} , B={x|6x8}
9. А={1 , 3 , 4} , B={7 ,5 }
10. А={y|2y 5} , B={x|1x6}
|
11. А={3 , 7 , 9} , B={2 ,5 }
12. А={y|3y 6} , B={x|1x4}
13. А={5 , 8 , 7} , B={1 ,4 }
14. А={y|2y 5} , B={x|1x3}
15. А={5 , 2 , 8} , B={4 ,6 }
16. А={y|2y 4} , B={x|2x5}
17. А={1 , 3 , 6} , B={2 ,7 }
18. А={y|3y 6} , B={x|2x6}
19. А={3 , 4 , 6} , B={4 ,7 }
20. А={y|4y 6} , B={x|1x7}
|
б) Жиындар алгебрасының тепе теңдiгi. Жиындар алгебрасының тепе-теңдiктерiн дәлелдеңiз.
Тапсырмалар варианты
1. A\ (BC)=( A\ B )\ C
2. A\ (B \ C)=( A\ B )(AC)
3. (AB)\C=( A\ C) (B\ C)
4. A(B\A)=
5. ( AB) = B \ A
6. AB=( AB )(AB)
7. AB= A B (AB)
8. A (B C)=( A B ) (A C)
9. A\ (BC)=( A\ B )(A\ C)
10. A (B\C)=(A B )\ (A C)
|
11. A (B C)=( A B ) (A C)
12. = ![](data:image/png;base64,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) ![](data:image/png;base64,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)
13. A B= A B
14. A\ B)\C=( A\ C )\ (B\ C)
15. A\ B= A (A B )![](data:image/png;base64,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)
16. A (B C)=( A B ) ( A C)
17. A\ (A\ B )= A B
18. A\ (BC)=( A\ B )(A\ C)
19. =
20. A (A B)= B
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2. Семестрлiк жұмыс. Сәйкестiк, бейнелеу, функциялар. Берiлген А және В жиындары ның арасындағы барлық мүмкін сәйкестіктерді атаңыз және оларды график түрінде кескіндеңіз.Олардың ішінен бейнелеу,функциональды бейнелеу және кері функциясы бар функцияларды көрсетіңіз.
Тапсырмалар варианты:
1.
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А = {a, b}, B = {c, d}
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8.
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А = {f, k}, B = {s,l}
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15.
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А = {7, 4}, B = {2, 8}
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2.
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А = {2,7}, B = {6, 2}
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9.
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А = {z, h}, B = {a, n}
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16.
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А = {u, f}, B = {7, 3}
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3.
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А = {b, a}, B = {e, h}
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10.
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А = {6, 3}, B = {8, 3}
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17.
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А = {4,9}, B = {w, f}
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4.
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А = {7, 2}, B = {2,8}
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11.
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А = {k, d}, B = {w, k}
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18.
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А = {s, k}, B = {5,1}
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5.
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А = {7, 4}, B = {g,l}
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12.
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А = {b, s}, B = {8, 2}
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19.
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А = {7, 2}, B = {9, 3}
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6.
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А = {d, n}, B = {5, 2}
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13.
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А = {1, 5}, B = {d, j}
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20.
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А = {4, 9}, B = {3, 6}
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7.
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А = {d,x}, B = {s, v}
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14.
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А = {d, c}, B = {z, b}
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21.
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А = {7, 4}, B = {g,l}
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3 Семестрлiк жұмыс Өзара бір мәнді сәйкестік және жиындардың қуаты.
Тапсырмалар варианты
Дәлелдеңіздер:
Ақырлы жиынның кез келген ішк
і жиыны ақырлы;
Саны ақырлы ақырлы жиындардың бірігуі ақырлы;
Саны ақырлы ақырлы жиындардың тура көбейтіндісі ақырлы;
Ақырлы жиын өзінің ешқандай ішкі жиынына эквивалентті емес;
Екі ақырлы жиын элементтерінің саны тең болса ғана эквивалентті;
Кез келген шексіз жиыннан саналымды ішкі жиын бөліп алуға болады;
Жиын өзінің қандай да бір меншікті ішкі жиынына эквивалентті болса ғана ақырсыз болады.
Саналымды жиынның кез келген ішкі жиыны саналымды немесе ақырлы;
Егер функцияның анықталу облысы саналымды болса,онда функцияның мәндер жиыны саналымды немесе ақырлы;
Квадрат пен кесіндінің нүктелер жиыны эквивалентті;
Саналымды немесе ақырлы С қуатты жиындардың бірігуі С қуатты;
Натурал сандардың саналымды тізбектер жиыны С қуатты ;
0 мен 1 құралған барлық саналымды тізбектер жиыны С қуатты ;
[0,1] сегментінде берілген барлық нақты функциялар жиындарының қуаты С дан үлкен;
Барлық жиын ішкі жиыны болатын жиын болмайды.
Жиынның барлық ішкі жиындарының жиынының қуаты сол жиынның өзінің қуатынан үлкен болады;
Екі шеңбердің нүктелерінің жиыны эквивалентті;
Мына жиындардың қуаты қандай болады:
Нақты сандардың барлық саналымды тізбектері?
Нақты сандар өсіндегі барлық үзіліссіз функциялар?
Нақты сандар түзуіндегі барлық монотонды функциялар?
4 Семестрлiк жұмыс . Жиындардағы бинарлы қатынастар.
Р бинарлы қатынасының анықталу облысы мен мәндер жиынын анықтаңыз. Оларды рефлексивтi, антирефлексивтi, симметриялы, антисиммтриялы, транзитивтi қасиеттерi бар ма?
Тапсырмалар варианттары
1. P R2, (x,y) P x2+y2 =1.
2. P (Z+)2, (x,y) P x2 = y
мұндағы, Z+ ={x Z| x>0}.
3. P Z2, (x,y) P x=- y.
4. P Z2 (x,y) P x-y жұп.
5. P Z2, (x,y) P x+y тақ.
6. P Z2, (x,y) P 2x=3y.
7. P Z2, (x,y) P x – y 2-ге еселі.
8. P R2, (x,y) P x+y 3 ке еселі.
9. P Z2, (x,y) P x2+y2=1.
10. P R2, (x,y) P x2 y.
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11. P R2, (x,y) P x2 = y.
12. P R2б (x,y) P y < x - 1.
13. P R2, (x,y) P x2+y2=4.
14. P R2, (x,y) P x+y= -2.
15. PR2, (x,y) P x-y Z.
16. PR2, (x, y) P y=|x|.
17. P Í (Z+)2, (x,y) Î P Ûx2 = y мұндағы,
Z+ ={x Î Z| x>0}.
18. P (Z+)2, (x,y) P ЕҮБ(x,y) 1, мұндағы, Z+={x Z| z>0}.
19. P Z2, (x,y) P y x-2.
20. P Z2, (x,y) P x=- y.
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5. Семестрлiк жұмыс.Логикалық функциялар және формулалар.
Берiлген логикалық функцияға ақиқаттық кесте құрыңыз. Қандай айнымылылар негiзгi, қандайы жалған?
Тапсырма варианттары
1. f(x, y, z) = (x V y) (z х)
2. f(x, y, z) = (x | y) (x z)
3. f(x, y, z) = xy (y z)
4. f(x, y, z) = xy zx
5. f(x, y, z) = (x y) (x V z x)
6. f(x, y, z) = (x y) V (z ~ x)
7. f(x, y, z) = (x V z) (x y)
8. f(x, y, z) = (z y) (x y)
9. f(x, y, z) = (x y) ~ (z x)
10.f(x, y, z) = (x ~ y) V (x z)
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11.f(x, y, z) = (z x) (xy V z)
12. f(x, y, z) = (x y) (y z)
13. f(x, y, z) = (x y) ~ (x V (z y))
14. f(x, y, z) = (x ) z
15. f(x, y, z) = x (y V z)
16. f(x, y, z) = (x y) V z
17. f(x, y, z) = x (z y) |y
18. f(x, y, z) = (x V y)(z x)
19. f(x, y, z) = (y Vx)|z
20. f(x, y, z) = ( x V y)(z x)
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Достарыңызбен бөлісу: |