The term "mutually exclusive" refers to a concept or a relationship between two or more items, events, conditions, or categories, emphasizing their complete and absolute separation or incompatibility with each other. When applied, it suggests that the presence or occurrence of one item or condition excludes the possibility of the other or others existing or happening at the same time, place, or circumstance.
In a categorical context, it means that the options or choices available are distinct and cannot coexist or overlap. For instance, if there are two mutually exclusive categories, selecting an item from one category automatically precludes selecting an item from the other.
This principle also applies to events and conditions. It implies that two events or conditions cannot occur simultaneously, as their contradictory nature prevents any overlap. For example, the events "raining" and "sunny" are mutually exclusive, as it is impossible for both to occur concurrently.
Moreover, the concept of mutual exclusivity is essential in mathematical probability where, for instance, two outcomes cannot both happen at once, resulting in assigning a probability value of zero to their joint occurrence.
To sum up, the term "mutually exclusive" denotes the complete separation, incompatibility, or non-overlapping nature of two or more items, events, conditions, or categories, emphasizing that the presence or occurrence of one precludes the presence or occurrence of the other.
