Principal of inclusion & exclusion for two sets by vishal maher
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The document discusses the principal of inclusion and exclusion for calculating the size of the union of two sets. It defines set cardinality as the number of elements in a set. The size of the union of two sets A and B can be calculated as |A| + |B| - |A intersection B|. An example demonstrates using this principal to find the size of the union of two sets where some elements are shared between the sets. The principal is then applied to a word problem about calculating the minimum number of programmers a company needs to hire for different types of jobs.
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The document explains the principle of inclusion and exclusion for calculating the cardinality (size) of the union of three sets. It defines the formula that the cardinality of the union of sets A, B and C equals the sum of the cardinalities of the individual sets minus the overlaps between pairs of sets plus the overlap of all three sets. It provides three examples applying this formula to solve for the size of unions of various sets.
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تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
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- 1. Principal Of Inclusion & Exclusion By Vishal Maher 1
- 2. Welcome To This Tutorial, In This Tutorial We Will Be Discuss About Principal Of Inclusion & Exclusion 2
- 4. Cardinality Of Set Number of elements present in a set A = {a, b, c, d, e} |A|= 5 And it is denoted by |A| 4
- 5. Operations On Two Set |A∪B| = |A| + |B| - |A∩B| 5
- 6. Ex. Let A={a, b, c, d, e} and B={c, e, f, h, k, m} find |A∪B| using Inclusion & Exclusion Principle of two set A∪B={a, b, c, d, e, f, h, k, m} |A ∪B|=9 A ∩B={c, e} |A ∩B|=2 |A|=5 |B|=6 |A ∪B|=|A|+|B|-|A ∩B| 9=5+6-2 9=11-2 9=9 This Is The Proof Of This Principle 6
- 7. Ex. A company want to hire 25 programmers to handle system programing job & 40 Programmers for application program, of those hire 10 will be expected to perform job of both types. How many programmer be hire by the company? Let A is set of system Programmers & B is set of application programmers |A|=25 |B|=40 |A ∩B|=10 |A ∪B| =|A|+|B|-|A ∩B| =25+40-10 =65-10 |A ∪B| =55 55 Programmers are to be hired by the company 7
- 8. Thank You 8