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Sets and operations
Membership, subsets, union, intersection, complement, and Venn diagrams.
A set is a collection; the operations combine them: union (either), intersection (both), difference, complement. Picture it: a Venn diagram; each region is a combination of memberships. Think it: the operations satisfy the same laws as and/or/not, sets and logic are the same algebra (Boolean algebra).
Çözümlü örnek · {1,2,3,4} union {3,4,5,6}
{1,2,3,4} union {3,4,5,6}
Adım adım
- A = \left\{1, 2, 3, 4\right\},\quad B = \left\{3, 4, 5, 6\right\}
The two sets.
- A \cup B = \left\{1, 2, 3, 4, 5, 6\right\}
Keep everything in either set.
- |A| = 4,\ |B| = 4,\ |A \cup B| = 6
Cardinalities. Note |A ∪ B| = |A| + |B| − |A ∩ B|.
Cevabı göster
Şimdi sen Bir problem seçin, ya da kendi probleminizi yazın ya da çizin. Her adım, bir resim, cevap sorulana kadar gizli.
Burada kullanılan sembolleri
Tüm tanım, resim ve her harfin anlamı için herhangi bir sembolü tıklayın.
Nasıl: Sets and operations
- Write each set explicitly, or describe it by a property.
- For a union keep everything in either; for an intersection only what is in both.
- Check |A ∪ B| = |A| + |B| − |A ∩ B|.
Sık sorulan sorular
Are some infinities bigger than others?
Yes. The integers and the rationals can be listed; the real numbers cannot (Cantor's diagonal argument), so there are strictly more reals than integers.
What is the difference between a relation and a function?
A relation pairs inputs with outputs freely; a function is a relation in which every input gets exactly one output.
More in Set Theory & Logic
Relations, functions and equivalenceCardinality and infinityLogic and methods of proof