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 onY
andX
is not functionally dependent on any subset ofY
.
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?