2. In set theory, let A and B be two sets, and the set composed of all elements belonging to set A and set B is called the intersection of set A and set B, and it is marked as A ∩ B. ..
3. Given two sets A and B, the set consisting of all their elements is called the union of set A and set B, marked as A∪B, and pronounced as A and B. ..
4. Complement set generally refers to absolute complement set, that is, generally let S be a set, A be a subset of S, and the set composed of all elements that do not belong to A in S is called absolute complement set of subset A in S. In other branches of set theory and mathematics, complement set has two definitions: relative complement set and absolute complement set.
Extended data:
First, set the characteristics.
1, certainty
Given a set, any element, whether it belongs to the set or not, must be one of them, and there is no ambiguity.
2. Interrelation
Any two elements in a collection are considered different, that is, each element can only appear once. Sometimes it is necessary to describe the situation where the same element appears many times. You can use multiset, where elements are allowed to appear multiple times.
3. Chaos
In a set, the state of each element is the same and the elements are out of order. You can define an order relation on the set. After defining the order relation, you can sort the elements according to the order relation. But as far as the characteristics of the set itself are concerned, there is no necessary order between elements.
Second, the operation law.
Exchange law: a ∩ b = b ∩ a; A∪B=B∪A
Law of constraint: a ∪ (b ∪ c) = (a ∪ b) ∪ c; A∩(B∩C)=(A∩B)∩C
The law of distribution duality: a ∩ (b ∪ c) = (a ∪ b) ∩ (a ∪ c); A ∪( B∪C)=(A∪B)∪( A∪C)
Duality law: (a ∪ b) c = a c ∪ b c; (A∩B)^C=A^C∪B^C
Identity: A∨? = A； A∩U=A
The law of seeking complement: a ∪ a' = u; A∩A'=？
Law of involution: A''=A
Idempotent law: a ∪ a = a; A∩A=A
Zero uniformity: a ∪ u = u; A∩？ =?
Law of absorption: a ∨ (a ∩ b) = a; A∩(A∪B)=A
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