About your example: that table doesn't fit the second database normalization (with your sample data, I presume that the C depends only on A). The second normalization form requires that:
No non-prime attribute in the table is functionally dependent on a
proper subset of a candidate key
(Wikipedia)
So the C depends on "A", which is a subset of your primary key. Your primary key is a special superkey. (dportas point out the fact that it can't be called candidate key, since it's not minimal).
Let's say more about the second normalization form. Transform your example a little for easy understanding, presume that there's a table CUSTOMER(customer_id, customer_name, address). A super key is a sub-set of your properties which uniquely determine a tube. In this case, there are 3 super key: (customer_id) ; (customer_id, customer_name) ; (customer_id, customer_name, address). (Customer name may be the same for 2 people)
In your case, you have determined (customer_id, customer_name) be the Primary Key. It violated the second form rules; since it only needs customer_id to determine uniquely a tube in your database. For the sake of theory accuration, the problem here raised from the choice of primary key(it's not a candidate key), though the same argument can be applied to show the redundance. You may find some useful example here.
The third normal form states that:
Every non-prime attribute is
non-transitively dependent on every
candidate key in the table
Let give it an example. Changing the previous table to fit the second form, now we have the table CUSTOMER(customer_id,customer_name, city, postal_code), with customer_id is primary key.
Clearly enough, "postal_code" depends on the "city" of customer. This is where it violated the third rule: postal_code depends on city, city depends on customer_id. That means postal_code transitively depends on customer_id, so that table doesn't fit the third normal form.
To correct it, we need to eliminate the transitive dependence. So we split the table into 2 table: CUSTOMER(customer_id, customer_name, city) and CITY(city, postal_code). This prevent the redundance of having too many tubes with the same city & postal_code.
