# Assessing statement about third normal form

Consider the following statements:

• A relation R, is in 3NF if every non-prime attribute of R, is fully functionally dependent on some key of R.

State True or False.

The answer given is true. But I think its false.

Example: Let `R(A,B,C)` be a relation with functional dependencies `{A→B, B→C}`.

Here `A` is the candidate key and both `B` and `C` are fully functionally dependent on `A` since `A→B` and also `A→C` right?

But this relation is clearly not in 3NF. Where am I wrong?

As per the definition I found here, the set of attributes `X` will be fully functionally dependent on the set of attributes `Y` if the following conditions are satisfied:

• `X` is functionally dependent on `Y` and
• `X` is not functionally dependent on any subset of `Y`.

Here `C` is functionally dependent on `A` and also `C` is not functionally dependent on any subset of `A`. So this would imply that `C` is fully functionally dependent on `A` right?

• Yes, you are right. Are you sure the question says "A relation R is in 3NF, if every.." and not "A relation R is in 2NF, if every.."? Commented Jan 15, 2018 at 15:54
• It says A relation R is in 3NF, if every non-prime attribute of R, is fully functionally dependent on some key of R. Commented Jan 15, 2018 at 16:16