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Introduction to Relations

As already said the notion of relation between two sets of objects is quite common and intuitively clear. If A is the set of all cities of the world and B is the set of countries of the world, then the relation R (is capital of) can be defined between two sets A and B. Thus, if x A and y B, then x is related to y by the relation R if x is capital of y, and write x R y. Since order is important we call R a relation from A to B. We can also define S from A to B by x S y if x is a city of y.

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