Complementary distribution in linguistics is the relationship between two different elements, where one element is found in a particular environment and the other element is found in the opposite environment. It often indicates that two superficially different elements are in fact the same linguistic unit at a deeper level. Comparing this concept to a coin, there is a "heads" side and a "tails" side. Although heads and tails differ from each other in appearance, and location, they are only two different faces of one and the same coin.
In some instances, more than two elements can be in complementary distribution with one another. Instead of an analogy with the two faces of a coin, consider an analogy with the six faces of a die (dice). Each face has a different appearance and location, but each is a part of one and the same cube.
There are cases where elements are in complementary distribution, but are not considered allophones. For example in English and (engma, written as "ng" in English) are in complementary distribution, since [h only occurs at the beginning of a syllable and only at the end. But because they have so little in common they are still considered separate phonemes.
The forms an and a function to work together like a team, in order to take care of every instance (environment) where the English indefinite article is needed. They are like two halves of a whole, or two different faces of one and the same coin.
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"Complementary distribution".
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