In logic, two mutually exclusive (or "mutual exclusive" according to some sources) 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. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Philosophers generally consider logical possibility to be the broadest sort of subjunctive possibility in modal logic. ...
In probability theory, events E1, E2, ..., En 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. Probability theory is the mathematical study of probability. ...
In short, mutual exclusivity implies that at most one of the events may occur. Compare this to the concept of being collectively exhaustive, which means that at least one of the events must occur. In probability theory, a set of events is collectively exhaustive if at least one of the events must occur. ...
Examples
A flipped coin coming up heads and the same coin coming up tails at the same time 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- or have the grade scaled).
When rolling a six-sided die, each of the outcomes 1, 2, 3, 4, 5 and 6 are mutually exclusive and collectively exhaustive, because no more than one outcome can occur simultaneously and they encompass the entire range of possible outcomes.
The logical operation A XOR B means A and B are mutually exclusive and cannot both be true at the same time.
In logic, two mutuallyexclusive (or "mutualexclusive" according to some sources) propositions are propositions that logically cannot both be true.
To say that more than two propositions are mutuallyexclusive may, depending on context mean that no two of them can both be true, or only that they cannot all be true.
A student passing a test and failing it are mutuallyexclusive (though someone can fail a test, retake it, and then pass- or have the grade scaled).
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