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Imkonsiz Hodisa (Impossible Event)
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| bet | 2/5 | | Sana | 11.06.2024 | | Hajmi | 268,92 Kb. | | #262522 |
Bog'liq Ilhom (Ehtimollik)Imkonsiz Hodisa (Impossible Event):
Hech qachon sodir bo'lmaydigan hodisa. Masalan, zar tashlashda 7 chiqishi: ∅\varnothing∅.
2. Hodisalar Algebrasi
Hodisalar algebrasi - bu hodisalar ustida amalga oshiriladigan amallar va ularning xossalarini o'rganadigan soha.
Hodisalar Ustida Amallar
Birlashtirish (Union):
A∪BA \cup BA∪B: A yoki B hodisasining sodir bo'lishi.
Misol: zar tashlashda 2 yoki 4 chiqishi: {2}∪{4}={2,4}\{2\} \cup \{4\} = \{2, 4\}{2}∪{4}={2,4}.
Kesish (Intersection):
A∩BA \cap BA∩B: A va B hodisalarining ikkalasi ham sodir bo'lishi.
Misol: zar tashlashda juft son chiqishi va 2 dan kichik son chiqishi: {2,4,6}∩{1,2}={2}\{2, 4, 6\} \cap \{1, 2\} = \{2\}{2,4,6}∩{1,2}={2}.
Komplement (Complement):
A′A'A′: A hodisasining sodir bo'lmasligi.
Misol: zar tashlashda 2 chiqmasligi: {1,3,4,5,6} \{1, 3, 4, 5, 6\}{1,3,4,5,6}.
Farq (Difference):
A∖BA \setminus BA∖B: A hodisasidan B hodisasini olib tashlash.
Misol: zar tashlashda 1, 2, 3 chiqishi va 2, 3 chiqishini olib tashlash: {1,2,3}∖{2,3}={1}\{1, 2, 3\} \setminus \{2, 3\} = \{1\}{1,2,3}∖{2,3}={1}.
Hodisalar Algebrasi Xossalari
Birlashtirish va Kesishning Assotsiativlik Xossasi:
A∪(B∪C)=(A∪B)∪CA \cup (B \cup C) = (A \cup B) \cup CA∪(B∪C)=(A∪B)∪C
A∩(B∩C)=(A∩B)∩CA \cap (B \cap C) = (A \cap B) \cap CA∩(B∩C)=(A∩B)∩C
Birlashtirish va Kesishning Kommutativlik Xossasi:
A∪B=B∪AA \cup B = B \cup AA∪B=B∪A
A∩B=B∩AA \cap B = B \cap AA∩B=B∩A
Distribitivlik Xossasi:
A∪(B∩C)=(A∪B)∩(A∪C)A \cup (B \cap C) = (A \cup B) \cap (A \cup C)A∪(B∩C)=(A∪B)∩(A∪C)
A∩(B∪C)=(A∩B)∪(A∩C)A \cap (B \cup C) = (A \cap B) \cup (A \cap C)A∩(B∪C)=(A∩B)∪(A∩C)
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