Event( A or B)
Union of two sets A and B denoted by A ∪ B contains all those elements which are either in A or in B or in both.
When the sets A and B are two events associated with a sample space, then‘ A ∪ B’ is the event‘ either A or B or both’. This event‘ A ∪ B’ is also called‘ A or B’.
Event‘ A or B’ = A ∪ B = { ω: ω ∈ A or ω ∈ B }.
Event‘ A and B’
Intersection of two sets A ∩ B is the set of those elements which are common to both A and B. i. e., which belong to both‘ A and B’.
If A and B are two events, then the set A ∩ B denotes the event‘ A and B’. Thus, A ∩ B = { ω: ω ∈ A and ω ∈ B }
Event‘ A but not B’
A – B is the set of all those elements which are in A but not in B. Therefore, the set A – B may denote the event‘ A but not B’. A – B = A ∩ B’