In logic, two mutually exclusive propositions are propositions that logically cannot both be true. To say that more than two propositions are mutually exclusive may, depending on context mean that no two of them can both be true, or only that they cannot all be true. The term pairwise mutually exclusive always means no two of them can both be true.

In probability theory, events E₁, E₂, ..., E_n are said to be mutually exclusive if the occurrence of any one them automatically implies the non-occurrence of the remaining n − 1 events. In other words, two mutually exclusive events cannot both occur.

Examples

• A flipped coin coming up heads and the same coin coming up tails are mutually exclusive events.
• A student passing a test and failing it are mutually exclusive (though someone can fail a test, retake it, and then pass).

See also

• excluded middle