Because events are a subset of the sample space , the relationships and operations between events can be treated as the relationships and operations between sets . The formulation and meaning of these relationships and operations in probability theory are given below.
　　(1) If , then event is said to contain event , or event is contained in event , or is a sub -event of The meaning is: if event occurs, event will inevitably occur. Obviously, .

　　(2) If , event and event are said to be equal . The meaning is: if event occurs, event will occur, and if event occurs, event will occur, that is, and .

　　(3) The event is called the sum ( or union ) of event and event Its meaning is: event occurs if and only if at least one of events and occurs. is sometimes also written as .
　　Similarly, is called the sum event of events , and x=1 is called the event of countable events .
　　(4) The event is called the product (or intersection ) of event and event Its meaning is: event occurs if and only if events and occur at the same time . Event is also denoted as .
　　Similarly,  is called the product event of  events  , and  is called the product event of countable events  . 

　　(5) The event is called the difference between event and event Its meaning is: event occurs if and only if event occurs and event does not occur.
　　 For example , in a die-throwing experiment , record the event

The number of points is an odd number , the number of points is less than ,

but

; ; .