A functional dependency X -> Y between attribute sets X and Y in relation R holds if:
A functional dependency X -> Y states that the value of X uniquely determines the value of Y. Formally, for any two tuples t1 and t2 in R, if t1[X] = t2[X], then t1[Y] must equal t2[Y].
A functional dependency X -> Y is termed a "trivial functional dependency" if and only if:
A functional dependency X -> Y is trivial if Y is a subset of X (e.g., AB -> A or A -> A), meaning it is satisfied by any legal relation instance automatically. Therefore, none of the first three statements is correct.
Which of Armstrong's Axioms states that if Y ⊆ X, then X -> Y holds?
The Reflexivity rule states that if Y is a subset of X, then X functionally determines Y (X -> Y).
According to Armstrong's Axioms, the Augmentation rule states that:
The Augmentation rule asserts that if X -> Y holds, then adding any set of attributes Z to both sides preserves the dependency: XZ -> YZ.
The Transitivity rule in Armstrong's Axioms states that:
Transitivity specifies that if X determines Y and Y determines Z, then X indirectly determines Z.