$1$a$)$ Let R be the relation on the set $\{1,2,3,4\}$ containing the ordered pairs $(2,1),$

$(2,3),(3,1),(3,4),(4,1),$ and $(4,3).$ Find the transitive closure of R$.$

$1$b$)$ In one state, automobile license plates must:

start with two digits $(0$ to $9),$ but the first cannot be a zero,

Followed by two upper$-$case letters $($A to Z$),$

Followed by a string of two to four digits $($leading zeros are allowed$).$

How many different license plates are possible?

$1$c$)$ identify each of these relations as one$-$to$-$one, one$-$to$-$many, many$-$to$-$many, many$-$to$-$one.

$\{(1,1),(2,5),(3,5),(3,8),(3,9),(4,7)\}$

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