Collectively exhaustive events

For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes.

The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., "MECE").

One example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin.

The union of both "even" and "odd" events give sample space of rolling the die, hence are collectively exhaustive.

Here are a few examples: The following appears as a footnote on page 23 of Couturat's text, The Algebra of Logic (1914):[1] In Stephen Kleene's discussion of cardinal numbers, in Introduction to Metamathematics (1952), he uses the term "mutually exclusive" together with "exhaustive":[3]