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A relation is a set of ordered pairs.
A function is a relation such that for each element there is one and only one second element.

Example:

{(1, 2), (4, 3), (6, 1), (5, 2)}

This is a function because every ordered pair has a different first element.

Example:

{(1, 2), (5, 6), (7, 2), (1, 3)}

This is a relation but not a function because when the first element is 1, the second element can be either 2 or 3.

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