Question $4(10$ points$)$

If $S=\{1,2,3,4\}$ and $T=\{5,6,7,8\}.$ Which of the following definitions describe functions with domain $S$ and codomain T$?$ Are the functions one$-$to$-$one, onto or bijective? If they are bijective, give the inverse function.

$($a$)\{(2,5),(4,6),(1,8),(3,5)\}$

$($b$)\{(3,5),(1,7),(4,8),(2,6)\}$

$($c$)\{(1,5),(4,8),(3,7),(1,6)\}$

$($d$)\{(4,5),(2,6),(3,8),(1,7)$