In high school, we learned concepts such as the laws of operations between sets , complete sets and complements . The following is a brief summary of the operation rules between events based on the set representation of events , the relationship and operations between sets , the sum, difference and product of events , mutually exclusive events and opposing events , etc.

　　Assume is an event in the same random experiment , then there is:

　　1. The operation rules of event union

　　(1) Commutative law : ;
　　(2) Associative law :

　　2. Operational rules of event intersection
　　(1) Commutative law : ;
　　(2) Associative law :

　　3. Mixed operation rules of event union and intersection
　　(1) First distributive law :

　　(2) The second distributive law :

　　Note : The above distributive law can be extended to the case of finite sets.
　　4. Opposite operations of events
　　If , then , that is, ( reflexive law )
　　5. Opposite operations of union and intersection ( De Morgan’s law )
　　(1) First duality law :

　　(2) The second duality law : .
　　 Note : The above duality law can be extended to the case of finite sets.