For 3NF first the table must be in 2NF plus we want to make sure that the non-ke

For 3NF first the table must be in 2NF plus we want to make sure that the non-key fields are dependent upon ONLY the PK and not other non-key fields for its existence. This is very similar to to 2NF except that now you are comparing the non-key fields to OTHER non-key fields. After all we know that the relationship to the PK is good because we established that in 2NF. An entity is in the third normal form if it is in the second normal form and all of its attributes are not transitively dependent on the primary key. Transitive dependence means that descriptor key attributes depend not only on the whole primary key but also on other descriptor key attributes that in turn depend on the primary key. In SQL terms the third normal form means that no column within a table is dependent on a descriptor column that in turn depends on the primary key.
For 3NF first the table must be in 2NF plus we want to make sure that the non-key fields are dependent upon ONLY the PK and not other non-key fields for its existence. This is very similar to to 2NF except that now you are comparing the non-key fields to OTHER non-key fields. After all we know that the relationship to the PK is good because we established that in 2NF.