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First of all, let's explain the term relation. Many everyday phenomena involve two quantities that can be related to each other by some rule of correspondence. In mathematics the term for such a rule of correspondence is called relation. Relations are often represented by mathematical equations and formulas.
Suppose you have a set A and a set B, so if a relation assigns to each element
in the set A exactly one element 
in the set B, then the function 
is in fact that relation.
Suppose you have a set A and a set B, so if a relation assigns to each element