Let R1 (A, B, C) and R2 (D, E) be two relational sachemas,

Home » Database » Database miscellaneous » Question

Let R₁ (A, B, C) and R₂ (D, E) be two relational sachemas, where the primary keys are shown underlined, and let C be a foreign key in R₁ referring to R₂. Suppose there is no violation of the above referential integrity constraint in the corresponding relational instances r₁ and r₂ .Which one of the following relational algebra expressions would necessarily produce an empty relation?

1. Π_D(r₂) - Π_C(r₁)
2. Π_C(r₁) - Π_D(r₂)
3. Π_D(r₁ ⋈ _{C ≠ D}(r₂)
4. Π_C(r₁ ⋈ _{C = D}(r₂)

Correct Option: B

C is an attribute in R1 but D is a key in K2.
So consider ΠC (r1) – ΠD (r2)
So the result of this query would be all those tuples

which are in ΠC (r1) but not in ΠD (r2). Since D is a key so it has all the possible values of C. So difference would always be empty. Hence (b) is correct.