When a sample space is partitioned into some mutually exclusive events such that their union is the sample space itself, then the events are called exhaustive events or collective events.
Suppose a die is tossed and the sample space is
Hence the events and are mutually exclusive because and . As shown in the figure, the three events and are exhaustive.
If is an event defined in the sample space , then is denoted by and is called a complement of .
The figure shows the event and the complement of .