You are given a schema R $=($student$\_$id$,$ student$\_$first, student$\_$last, course$\_$id$)$ that models students and the classes that they are taking. We want to know if R is in $3$NF$.$ As a reminder, a relation is in $3$NF if every non$-$key attribute of R is determined by the key and nothing but the key.

Propose a potential key of R$.$ For this key, please answer the following questions:

Is every non$-$key attribute determined by the key?

Is every non$-$key attribute determined by the whole key?

Is every non$-$key attribute determined by nothing but the key?

Are we in $3$NF$?$ If not, how can we decompose our relation to be in $3$NF$?$