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In Linguistics, valence refers to the number of arguments that a verb can take. For example, a monovalent verb (such as "sleep", for example) cannot take a direct object. ("He sleeps," versus *"He sleeps it.") A trivalent verb, for example "give", has three arguments: the giver, the givee, and the thing given.
For a better explanation, see verb.
Valence is the name of several places in France: