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 ’