What are the basic operations of a set?

Duality law: (a ∪ b) c = a c ∪ b c; (A∩B)^C=A^C∪B^C。

Other setting operation rules:

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)

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

Extended data:

Characteristics of sets

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.

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