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In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
However, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition. This is equivalent to saying that the converse of a definition is true. Thus, the statement "If I am a triangle, then I am a three-sided polygon" is logically equivalent to "If I am a three-sided polygon, then I am a ...
The MECE principle (mutually exclusive and collectively exhaustive) is a grouping principle for separating a set of items into subsets that are mutually exclusive ...
Compare this to the concept of a set of mutually exclusive events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.) The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., "MECE"). The events 1 and 6 are mutually exclusive ...
George Boole, closely following analogy with ordinary mathematics, premised, as a necessary condition to the definition of x + y, that x and y were mutually exclusive. Jevons , and practically all mathematical logicians after him, advocated, on various grounds, the definition of logical addition in a form that does not necessitate mutual ...
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Venn diagram showing the union of sets A and B as everything not in white. In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as