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.."? Jan 15 '18 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. Jan 15 '18 at 16:16