Number of Elements in an Identity Function
Question
The number of elements of an identity function defined on a set containing four elements is __________.
Solution
Let the set be
\[ A=\{a,b,c,d\} \]An identity function on a set maps every element to itself.
Therefore, the identity function is
\[ I=\{(a,a),(b,b),(c,c),(d,d)\} \]Thus, the identity function contains one ordered pair for each element of the set.
Since the set has \(4\) elements, the identity function also contains \(4\) ordered pairs.