If A and B are sets, the union of A and B is a set containing all elements of A and all elements of B, but no other elements. The union of a and b is usually written as "A∪B" and pronounced as "a and b", which is expressed in symbolic language, namely: A∪B={x|x∈A, or x∈B}

Formally, X is an element of A∪B if and only if X is an element of A or X is an element of B. ..

Algebraic properties of union sets;

Binary union (union of two sets) is a combination operation, that is, A ∨( B∪C)=(A∪B)∪C, in fact, A∪B∪C is also equal to these two sets, so parentheses can be omitted when only union operation is performed. Similarly, the union operation satisfies the commutative law, that is, the order of the sets is arbitrary.

Empty set is the unit element of union operation. Namely. ∪A=A = A. For any set A, an empty set can be regarded as the union of zero sets.

Joint operation combines intersection operation and complement set operation, and integrates any power into Boolean algebra. For example, union and intersection satisfy the distribution law, and these three operations satisfy De Morgan's law. If the union operation is replaced by symmetric difference operation, the corresponding Boolean ring can be obtained.