Question $1.$ Consider the following problem $($The Student Dormitory Problem:

Given a set of n students, $\{$P$1,$ P$2,.,$ Pn$\},$ and a list of pairs of students who dislike each other, is it possible to split the students into three dormitories, D$1,$ D$2$ and D$3$ so that no dormitory contains pair of students who dislike each other?

$($a$)$ Prove that the Student Dormitory Problem is in NP$.$

For instance, Q of the Student Dormitory Problem, describe what a solution to Q would like and how it could be verified in polynomial time.