A dichotomy is any splitting of a whole into exactly two non-overlapping parts.
In other words, it is a partition In mathematics, a partition of a set X is a division of X into non-overlapping "parts" or "blocks" or "cells" that cover all of X. More formally, these "cells" are both collectively exhaustive and mutually exclusive with respect to the set being partitioned of a whole (or a set) into two parts (subsets) that are:
- mutually exclusive : nothing can belong simultaneously to both parts, and
- jointly exhaustive : everything must belong to one part or the other.
The two parts thus formed are complements. In logic Logic, from the Greek λογική is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its fundamental place in philosophy. It became part of the classical trivium, a fundamental part of a, the partitions are opposites if there exists a proposition In logic and philosophy, proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or (b) the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence. Propositions in either case are intended to be truth-bearers, that is, they are either true or false such that it holds over one and not the other.
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