Intuitively, a relation is a formula, (*x*, *y*, *z*). We say that *a, b, c* are related according to (*x*, *y*, *z*) just in case (*a*, *b*, *c*) is true. Influenced by the set theorist who wants to realize “everything” (even formulae) as some set, the modern mathematician views relations *extensionally* (by what they contain) *as sets*. For example, (*x*, *y*, *z*) naturally defines this set, its *extension:* {*x*, *y*, *z* : (*x*, *y*, *z*)}. One goes one step further and forgets the role of . As a result, we give a totally extensional definition of a relation as a set of tuples, disregarding how it may have been formed by a “defining property”.

**1.2.0.4 Definition**. A *binary relation* —or simply *relation—R ...*

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