Correct : b

The tuple relational calculus expression E = {⟨u⟩ | ∃v ∃w ⟨u, v⟩ ∈ R ∧ ⟨v, w⟩ ∈ S} says: find all values u such that there exists a value v where the pair (u, v) appears in R, and that same v along with some w appears in S.
Reading this carefully — u maps to R.P, v maps to R.Q (from the first condition), and v also maps to S.X (from the second condition). So the link between R and S is that R.Q must equal S.X. The output is only u, which is R.P. This gives the relational algebra expression Π_P(R ⋈_R.Q=S.X S).
Option A uses the join condition R.P = S.X which is wrong — R.P is what we output, not what we join on. Option C joins on R.P = S.Y which is also wrong on both attribute sides. Option D joins on S.Y = R.Q which uses the wrong S attribute — it should be S.X not S.Y. Option B joins on S.X = R.Q which is exactly the correct condition, and projects onto P from R. Writing the relations in different order inside the join does not change the result since natural join is commutative.
Correct answer: B ✓