Given two sets A and B, the set formed by merging all their elements is called the union set of set A and set B, marked as A∪B, and pronounced as A and B..

In set theory, let A and B be two sets, which are composed of all elements belonging to set A and set B, called the intersection of set A and set B, and marked as A ∩ B.

The intersection of (1) set {1, 2,3} and {2,3,4} is {2,3}. That is {1, 2,3} ∩ {2,3,4} = {2,3}.

(2) The number 9 does not belong to the prime set {2, 3, 5, 7,1,...} and the odd set {1, 3, 5, 7, 9,1,...} {x|x is prime }∩{x|x is odd}.

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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.