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Examine which of the following relations...

Examine which of the following relations (defined on subsets of Z) are functions
(i) f = {(2, 1), (2, 3), (4, 3), (1, 2)}
(ii) g = {(2, 1), (4, 2), (6, 3), (8,4), (10, 5)}

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(i) Given f = {(2, 1), (2, 3), (4, 3), (1, 2)}
Since (2, 1), and (2, 3) have same first element i.e., 2 has two images 1 and 3, so f is not a function.
(ii) Given g = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5)}
Since no two first elements of ordered pairs are same, hence g is a function.
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