Consider a relational database schema with two relations 𝑅(𝑃,𝑄) and…

To find the equivalent relational algebra expression, we analyze the Tuple Relational Calculus (TRC) expression:

E = { ⟨u⟩ | ∃v ∃w (⟨u, v⟩ ∈ R ∧ ⟨v, w⟩ ∈ S) }

1. Identify Attributes: Relation R has attributes (P, Q) and S has attributes (X, Y).

2. Map Variables: The tuple ⟨u, v⟩ ∈ R implies u corresponds to P and v corresponds to Q. The tuple ⟨v, w⟩ ∈ S implies v corresponds to X and w corresponds to Y.

3. Determine Join Condition: The variable v is common to both relations. Thus, the join condition is R.Q = S.X.

4. Determine Projection: The result is projected on u, which corresponds to attribute P of relation R.

5. Construct Expression: The equivalent expression is Π_P (S ⋈_{S.X=R.Q} R) or Π_P (R ⋈_{R.Q=S.X} S).

Option B matches this structure: Π_P (S ⋈_{S.X=R.Q} R).