Example 14
Show that a one-one function \(f : \{1, 2, 3\}
\to \{1, 2, 3\}\) must be onto.
Solution
Since \(f\) is one-one, three elements
of \(\{1, 2, 3\}\) must be taken to 3
different elements of the co-domain \(\{1, 2,
3\}\) under \(f\).
Hence, \(f\) has to be onto.