Круги Эйлера - это удобный инструмент для визуализации и решения задач по алгебре логики. Они позволяют наглядно представить множества и отношения между ними, что значительно упрощает понимание логических операций и формулирование решений.
Как использовать круги Эйлера:
1. Определение множеств: Каждое множество изображается кругом.
2. Необходимо изобразить отношения между понятиями в кругах Эйлера. Понятия могут быть между собой совместимыми и несовместимыми.
Отношения совместимости: равнозначность, перекрещивание (пересечение), подчинение.
Равнозначность — объем одного понятия полностью совпадает с объемом другого понятия.
Перекрещивание (пересечение) — объемы понятий частично совпадают.
Подчинение — объем одного полностью входит в объем другого, но не исчерпывает его.
При подчинении подчиняющее понятие называется родом по отношению к подчиненному, а подчиненное — видом по отношению к починяющему. (Понятие «животное» является родовым по отношению к видовому «слон»).
Отношения несовместимости: соподчинение, противоположность и противоречие.
Соподчинение — объемы двух понятий А и В произвольным образом входят в объем третьего родового понятия С.
Противоположность — объемы понятий А и В занимают наиболее удаленные относительно некоего качества позиции.
Противоречие — объемы понятий А и В полностью исчерпывают объем родового понятия С.
Даны два множества: A = {1, 2, 3, 4} и B = {3, 4, 5, 6}. Найдите объединение A и B (A ∪ B)
1. Изображаем круги: Рисуем два круга, один для A, другой для B.
2. Заполняем круги: Вписываем элементы множества A в первый круг, а элементы множества B – во второй.
3. Пересечение: Элементы 3 и 4 входят в оба множества, поэтому их закрашиваем в области пересечения кругов.
4. Объединение: Множество A ∪ B - это все элементы, находящиеся внутри обоих кругов. В итоге, A ∪ B = {1, 2, 3, 4, 5, 6}.
В языке запросов поискового сервера для обозначения логической операции «ИЛИ» используется символ «|», а для обозначения логической операции «И» –– символ «&».
В таблице приведены запросы и количество найденных по ним страниц некоторого сегмента сети Интернет.
|
Запрос |
Найдено страниц (в тысячах) |
|
Шахматы & Теннис |
880 |
|
Шахматы |
3100 |
|
Теннис |
4400 |
Какое количество страниц (в тысячах) будет найдено по запросу
Шахматы | Теннис?
Считается, что все запросы выполнялись практически одновременно, так что набор страниц, содержащих все искомые слова, не изменялся за время выполнения запросов.
Представим таблицу в виде кругов Эйлера.
Прономеруем каждую область:
Тогда задача — найти количество элементов N в областях 1+2+3: N. По таблице известно:
N2 = 880 (1),
N1 + N2 = 3100 (2),
N2 + N3 = 4400 (3).
Выражаем:
N = (2)+(3)-(1) = 4400 + 3100 - 880 = 6620
|
Country / Страна |
Full name / ФИО |
Award / Награда |
|
Russia |
Bystrov Maksim |
Absolute Winner in Experimental Examination / Absolute Winner / National Diamond |
|
Russia |
Bakhvalov Andrey |
Absolute Winner in Theory and Modelling |
|
Uzbekistan |
Ildar Khashaev |
National Diamond |
|
Tajikistan |
Salimov Husanjon |
National Diamond |
|
Turkmenistan |
Jumadurdy Nuryyev |
National Diamond |
|
Belarus |
Alina Polonskaya |
National Diamond |
|
Kazakhstan |
Bissimbi Doszhan |
National Diamond |
|
Qatar |
ADITYA VIVEK |
National Diamond |
|
Armenia |
Arsen Aghayan |
National Diamond |
|
Kyrgyzstan |
Abdiev Askar |
National Diamond |
|
Peru |
Luis Fabian Sanchez Romero |
National Diamond |
|
Syria |
Bahaa Aldeen Melhem |
National Diamond |
|
Montenegro |
Jovan Jankovic |
National Diamond |
|
Pakistan |
Muhammad Ismail Naqi |
National Diamond |
|
Cuba |
Carlos Daniel Chaviano González |
National Diamond |
|
Ghana |
AFRIYIE GRACIOUS ANNOR |
National Diamond |
|
Abkhazia |
Agrba Arseniy Aslanovich |
National Diamond |
|
Egypt |
Mohamed Ahmed |
National Diamond |
|
Indonesia |
Zakkaha Fauzan Premos |
National Diamond |
|
India |
Arsh Bhatnagar |
National Diamond |
|
Country / Страна |
Special prize / Награда |
|
Armenia |
3rd place |
|
Kazakhstan |
2nd place |
|
Belarus |
1st place |
|
Russia |
Grand Prix |
|
Country / Страна |
Full name / ФИО |
Award / Награда |
|
Belarus |
Alina Polonskaya |
1st place |
|
Belarus |
Ivanov Ilya Alekseevich |
1st place |
|
Kazakhstan |
Bissimbi Doszhan |
1st place |
|
Kazakhstan |
Nursagatov Margulan |
1st place |
|
Kazakhstan |
Pshenbayev Amir |
1st place |
|
Russia |
Bakhvalov Andrey |
1st place |
|
Russia |
Bystrov Maksim |
1st place |
|
Russia |
Pulyayevskiy Andrey |
1st place |
|
Russia |
Chernous Maksim |
1st place |
|
Syria |
Abdul Hadi Chmachan |
1st place |
|
Syria |
Bahaa Aldeen Melhem |
1st place |
|
Armenia |
Arsen Aghayan |
2nd place |
|
Armenia |
Artyom Gasparyan |
2nd place |
|
Armenia |
Smbat Poghosyan |
2nd place |
|
Belarus |
Artem Levko |
2nd place |
|
Belarus |
Mihail Khyrsin |
2nd place |
|
Belarus |
Yersh Andrei |
2nd place |
|
Kazakhstan |
Kazymbek Iliyas |
2nd place |
|
Kazakhstan |
Kim Artur |
2nd place |
|
Kazakhstan |
Barlybayev Nurassyl |
2nd place |
|
Kazakhstan |
Dyussebaliyev Beibarys |
2nd place |
|
Kazakhstan |
Abdykadyr Tair Omirtayuly |
2nd place |
|
Kyrgyzstan |
Abdiev Askar |
2nd place |
|
Montenegro |
Jovan Jankovic |
2nd place |
|
Pakistan |
Muhammad Ismail Naqi |
2nd place |
|
Pakistan |
Muhammad Somaan Fater |
2nd place |
|
Peru |
Luis Fabian Sanchez Romero |
2nd place |
|
Uzbekistan |
Ildar Khashaev |
2nd place |
|
Armenia |
Armen Gazazyan |
3rd place |
|
Armenia |
Narek Galstyan |
3rd place |
|
Armenia |
Narek Movsisyan |
3rd place |
|
Armenia |
Arsen Asatryan |
3rd place |
|
Cuba |
Josué Pablo Moya Tornet |
3rd place |
|
Cuba |
Carlos Daniel Chaviano González |
3rd place |
|
Kazakhstan |
Sovetkhanov Maksat |
3rd place |
|
Kazakhstan |
Akberdi Alibi Azamatuly |
3rd place |
|
Kazakhstan |
Kabdullov Nurali Dauletovich |
3rd place |
|
Kyrgyzstan |
Anaraly uulu Emir |
3rd place |
|
Kyrgyzstan |
Baratali Bektur |
3rd place |
|
Kyrgyzstan |
Emilbekov Aitegin |
3rd place |
|
Kyrgyzstan |
Turdukeev Atai |
3rd place |
|
Pakistan |
Rabia Shahzad |
3rd place |
|
Pakistan |
Raem Anis Rahman |
3rd place |
|
Pakistan |
Muhammad Umar Danish |
3rd place |
|
Peru |
Rivera Lopez David Summer |
3rd place |
|
Syria |
Anas Mayya |
3rd place |
|
Syria |
Mohamad Eid Al Aktaa |
3rd place |
|
Syria |
Ziad Badleh |
3rd place |
|
Tajikistan |
Ghulomzoda Huseini |
3rd place |
|
Tajikistan |
Salimov Husanjon |
3rd place |
|
Turkmenistan |
Jumadurdy Nuryyev |
3rd place |
|
Turkmenistan |
Mekangeldi Janmyradov |
3rd place |
|
Armenia |
Gor Hasratyan |
Honorable mention |
|
Armenia |
Vahe Melkonyan |
Honorable mention |
|
Cuba |
Roimer Capote Brizuela |
Honorable mention |
|
Cuba |
Sergio Daneel Santiesteban |
Honorable mention |
|
Cuba |
Rosmary Fernández Tamayo |
Honorable mention |
|
Ghana |
AFRIYIE GRACIOUS ANNOR |
Honorable mention |
|
Ghana |
AGYEMAN NANA YAW AGYAPONG |
Honorable mention |
|
Kazakhstan |
Tyulyubay Nurali |
Honorable mention |
|
Kazakhstan |
Mirkamalov Nurassyl Baurzhanuly |
Honorable mention |
|
Kazakhstan |
Tamirlan Makishev Erbolovich |
Honorable mention |
|
Tajikistan |
Ashraf Anvari |
Honorable mention |
|
Tajikistan |
Haidari Muhammadrobe |
Honorable mention |
|
Tajikistan |
Mamurov Mukhammadyosin |
Honorable mention |
|
Turkmenistan |
Aynabat Veljanova |
Honorable mention |
|
Uzbekistan |
Abdulloh Mamaniyozov |
Honorable mention |
|
Uzbekistan |
Rajabov Dilshodbek |
Honorable mention |
|
Country / Страна |
Full name / ФИО |
Award / Награда |
|
Belarus |
Alina Polonskaya |
Gold medal |
|
Kazakhstan |
Bissimbi Doszhan |
Gold medal |
|
Kazakhstan |
Nursagatov Margulan |
Gold medal |
|
Russia |
Bakhvalov Andrey |
Gold medal |
|
Russia |
Bystrov Maksim |
Gold medal |
|
Russia |
Pulyayevskiy Andrey |
Gold medal |
|
Russia |
Chernous Maksim |
Gold medal |
|
Belarus |
Ivanov Ilya Alekseevich |
Silver medal |
|
Kazakhstan |
Pshenbayev Amir |
Silver medal |
|
Armenia |
Arsen Aghayan |
Silver medal |
|
Armenia |
Artyom Gasparyan |
Silver medal |
|
Belarus |
Artem Levko |
Silver medal |
|
Belarus |
Mihail Khyrsin |
Silver medal |
|
Belarus |
Yersh Andrei |
Silver medal |
|
Kazakhstan |
Kim Artur |
Silver medal |
|
Kyrgyzstan |
Abdiev Askar |
Silver medal |
|
Peru |
Luis Fabian Sanchez Romero |
Silver medal |
|
Armenia |
Armen Gazazyan |
Bronze medal |
|
Armenia |
Narek Galstyan |
Bronze medal |
|
Armenia |
Narek Movsisyan |
Bronze medal |
|
Armenia |
Arsen Asatryan |
Bronze medal |
|
Kyrgyzstan |
Anaraly uulu Emir |
Bronze medal |
|
Kyrgyzstan |
Baratali Bektur |
Bronze medal |
|
Kyrgyzstan |
Turdukeev Atai |
Bronze medal |
|
Peru |
Rivera Lopez David Summer |
Bronze medal |
|
Tajikistan |
Ghulomzoda Huseini |
Bronze medal |
|
Tajikistan |
Salimov Husanjon |
Bronze medal |
|
Turkmenistan |
Jumadurdy Nuryyev |
Bronze medal |
|
Turkmenistan |
Mekangeldi Janmyradov |
Bronze medal |
|
Armenia |
Gor Hasratyan |
Bronze medal |
|
Kyrgyzstan |
Emilbekov Aitegin |
Honorable mention |
|
Armenia |
Vahe Melkonyan |
Honorable mention |
|
Tajikistan |
Ashraf Anvari |
Honorable mention |
|
Tajikistan |
Haidari Muhammadrobe |
Honorable mention |
|
Uzbekistan |
Abdulloh Mamaniyozov |
Honorable mention |
|
Uzbekistan |
Rajabov Dilshodbek |
Honorable mention |
|
Qatar |
ADITYA VIVEK |
Honorable mention |
|
Qatar |
Omar Mohammed A I AI-Emadi |
Honorable mention |
|
Uzbekistan |
Ravshanov Ozodbek |
Honorable mention |
|
Uzbekistan |
Sadullaev Javohir |
Honorable mention |
| № | Participant | Country | Award |
| 1 | Maksim Chayka | Russia | Gold Medal |
| 2 | Daniil Gavrilov | Russia | Gold Medal |
| 3 | Egor Potapov | Russia | Gold Medal |
| 4 | Vyacheslav Bobkov | Russia | Gold Medal |
| 5 | Ivan Likhokon | Russia | Gold Medal |
| 6 | Andrey Bakhvalov | Russia | Gold Medal |
| 7 | Maksim Bystrov | Russia | Gold Medal |
| 8 | Aleksey Gashpar | Russia | Gold Medal |
| 9 | Mikhail Muravyev | Russia | Gold Medal |
| 10 | Fansen Candra Funata | Indonesia | Gold Medal |
| 11 | Aleksandr Anisimov | Russia | Gold Medal |
| 12 | Uladzislau Andreikavets | Belarus | Gold Medal |
| 13 | Andrey Knyazev | Russia | Silver Medal |
| 14 | Anastasiya Pliasunkova | Belarus | Silver Medal |
| 15 | Maksim Chernous | Russia | Silver Medal |
| 16 | Muhammad Arif Khalfaani Ismail | Indonesia | Silver Medal |
| 17 | Jovan Jankovic | Montenegro | Silver Medal |
| 18 | Ahmad Nafi Ramadhan | Indonesia | Silver Medal |
| 19 | Mikhail Prokhorchenko | Russia | Silver Medal |
| 20 | Manuel Mario Nadir Gilvonio Saez | Peru | Silver Medal |
| 21 | Anas Ali Mayya | Syria | Silver Medal |
| 22 | Husanjon Salimov | Tajikistan | Silver Medal |
| 23 | Jaloliddin Boymakhammadov | Uzbekistan | Silver Medal |
| 24 | Luis Fabian Sanchez Romero | Peru | Silver Medal |
| 25 | Bahaa Aldeen Melhem | Syria | Silver Medal |
| 26 | Javohir Sultanov | Uzbekistan | Silver Medal |
| 27 | Mohamad Eid Alaktaa | Syria | Silver Medal |
| 28 | Nestor Andre Quinteros Rodriguez | Peru | Bronze Medal |
| 29 | Mufeed Mohamed Jalkhi | Syria | Bronze Medal |
| 30 | Huseini Ghulomzoda | Tajikistan | Bronze Medal |
| 31 | Aliaksander Aheuey | Belarus | Bronze Medal |
| 32 | Ziad Jalal Badleh | Syria | Bronze Medal |
| 33 | Muh Zaidan Naja | Indonesia | Bronze Medal |
| 34 | Huda Jerby | Syria | Bronze Medal |
| 35 | Jasurbek Gulomjonov | Uzbekistan | Bronze Medal |
| 36 | Mohammad Nader Aldalati | Syria | Bronze Medal |
| 37 | David Summer Rivera Lopez | Peru | Bronze Medal |
| 38 | Lachyn Hydyrova | Turkmenistan | Bronze Medal |
| 39 | Jumadurdy Nuryyev | Turkmenistan | Bronze Medal |
| 40 | Hazem Emadel Din Abdel Mughni Muhammad Hassan | Egypt | Bronze Medal |
| 41 | Mirshodjon Rajabov | Uzbekistan | Bronze Medal |
| 42 | Majd Amer | Syria | Bronze Medal |
| 43 | William Christian Gani | Indonesia | Bronze Medal |
| 44 | Mohamad Ali | Syria | Bronze Medal |
| 45 | Elias Koschier | Austria | Bronze Medal |
| 46 | Arslan Jumayev | Turkmenistan | Bronze Medal |
| 47 | Abdelrahman Waleed Hamdy Mohammed Ismail | Egypt | Bronze Medal |
| 48 | Emir Garajayev | Turkmenistan | Bronze Medal |
| 49 | Belal Bahaa Hamouda Mohamed Hamouda | Egypt | Honorable Mention |
| 50 | Mahmoud Ibrahim | Syria | Honorable Mention |
| 51 | Davut Alybayev | Turkmenistan | Honorable Mention |
| 52 | Timur Tahil | Belarus | Honorable Mention |
| 53 | Sannidhya Singh | India | Honorable Mention |
| 54 | Asset Kdyr | Kazakhstan | Honorable Mention |
| 55 | Meirzhan Kudabaev | Kazakhstan | Honorable Mention |
| 56 | Ibraheem Khan | Pakistan | Honorable Mention |
| 57 | Nazgul Sandybekova | Kazakhstan | Honorable Mention |
| 58 | Alibi Turaly | Kazakhstan | Honorable Mention |
| № | Participant | Country | Special Prize |
| 1 | Maksim Chayka | Russia | Absolute Winner |
| 2 | Maksim Chayka | Russia | National Diamond |
| 3 | Fansen Candra Funata | Indonesia | National Diamond |
| 4 | Uladzislau Andreikavets | Belarus | National Diamond |
| 5 | Jovan Jankovic | Montenegro | National Diamond |
| 6 | Manuel Mario Nadir Gilvonio Saez | Peru | National Diamond |
| 7 | Anas Ali Mayya | Syria | National Diamond |
| 8 | Husanjon Salimov | Tajikistan | National Diamond |
| 9 | Jaloliddin Boymakhammadov | Uzbekistan | National Diamond |
| 10 | Lachyn Hydyrova | Turkmenistan | National Diamond |
| 11 | Hazem Emadel Din Abdel Mughni Muhammad Hassan | Egypt | National Diamond |
| 12 | Elias Koschier | Austria | National Diamond |
| 13 | Sannidhya Singh | India | National Diamond |
| 14 | Asset Kdyr | Kazakhstan | National Diamond |
| 15 | Meirzhan Kudabaev | Kazakhstan | National Diamond |
| 16 | Ibraheem Khan | Pakistan | National Diamond |
| № | Country | Special Prize |
| 1 | Russia | Best team result. Grand Prix |
| 2 | Indonesia | Best team result. The 1st place |
| 3 | Syria | Best team result. The 2nd place |
| 4 | Belarus | Best team result. The 3rd place |
