Let R is a relation schema and X, Y ⊆ R. "If Y ⊆ X, then X → Y" represents which of the following inference rules?

Let R is a relation schema and X, Y ⊆ R. "If Y ⊆ X, then X → Y" represents which of the following inference rules? Correct Answer Reflexive

The correct answer is option 2.

Concept:

Let us consider X, Y, and Z are sets of attributes in a relation to R.

Reflexive Functional Dependencies:

Let R be a relation scheme and let X ⊆ R and Y ⊆ R. We say that a relation instance r(R) satisfies a functional dependency X → Y if for every pair of tuples t1 ∈ r and t2 ∈ r if t1 = t2 then t1 = t2. (or)

Reflexivity:

If X is a set of attributes, and Y is a set of attributes that are completely contained in X, then X implies Y.

If Y is a subset of X, then X → Y

Example:

Mobile, Name →Name

Augmentation:

If X implies Y, and Z is a set of attributes, then if X implies Y, then XZ implies YZ.

If X → Y, then XZ → YZ

Example:

Id→Name then Id, address→Name, address

Transitivity:

If X implies Y and Y imply Z, then X implies Z.

If X → Y and Y → Z, then X → Z

Example:

Id→contact_number and Contact_number→ state then Id→Contact_number, state.

Hence the correct answer is Reflexive.