Part AProblem $5.$ Set$-$Builder Notation $(8$ points$)$

$($a$)[4$ pts$.]$ Express the set:

$S=\{zinZ|(0z)vv((zmod4=3{)}^{{?}^{?}}(z12))\}$

by writing each item in the set $($e$.$g$.\{1,2,3\}).$ Feel free to use $...$ for infinite patterns.

$($b$)[4$ pts$.]$ Express the set $T$ of all natural numbers which are multiples of $4$ and divisible by $3$

using set builder notation.

Solution: