Question 7 [12 marks]. Let S = \{a, b, c, d\}, and let $f_1$: S $\to$ S, $f_2$: S $\to$ S and $f_3$: S $\to$ S be the following functions:
$f_1$ = \{ (a, c), (b, a), (c, d), (d, b) \},
$f_2$ = \{ (a, b), (b, d), (c, d), (d, c) \},
$f_3$ = \{ (a, b), (b, b), (c, b), (d, b) \}.
For each of the functions $f_1$, $f_2$, $f_3$, determine whether it is injective, surjective,
and/or bijective. In the case of negative answers, provide a suitable reason.
[12]