A vniversity registrar has $n$ student and m courses for which she needs to assign final exam times, using $K$ time slots. If $x$ and $y$ are two different courses, and there is any student in both courses, she may not give them the same time slot. Let SCHED be the set of tuples $(s,C,A,K)$ such that:

$-$S$,$ is list of students

$-c,$ is a list of $$ourses

$A,$ is the set of pairs $(S,C)$ in $SC$ such student $3$ is in course $c,$ and

$K$ is the number of time slots, such that

It is possible to assign each course in Cto a time slot with no student being assigned two couses at the same time

Prove that this language is NP$-$Complete