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Set theory is the mathematical study of collections of distinct objects. Operations like union (∪), intersection (∩), and difference (−) describe how sets relate to each other and underlie all of modern mathematics and computer science.
Wzór
Union: A∪B = {x | x ∈ A or x ∈ B} | Intersection: A∩B = {x | x ∈ A and x ∈ B}
- ∪
- Union — All elements in either set
- ∩
- Intersection — Elements in both sets
- −
- Difference — Elements in first set but not second
Przewodnik krok po kroku
- 1Union A∪B: all elements in A or B (or both)
- 2Intersection A∩B: elements in both A and B
- 3Difference A−B: elements in A but not B
- 4Symmetric difference A△B: in A or B but not both
Rozwiązane przykłady
Wejście
A={1,2,3,4,5}, B={3,4,5,6,7}
Wynik
A∪B={1,2,3,4,5,6,7}, A∩B={3,4,5}, A−B={1,2}
Często zadawane pytania
What is the complement of a set?
The complement of A (denoted A' or Aᶜ) contains all elements in the universal set that are NOT in A.
What is the difference between union and intersection?
Union combines all elements from both sets. Intersection finds only the elements that appear in both sets.
How is set theory used in programming?
Sets are used in databases (SQL joins use union/intersection), algorithms, graph theory, and logic. They're fundamental to computer science theory.
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