ITPEC FE Subject A April 2026 Question 21

PTY, QTY, STY — every candidate key must contain both T and Y.

Start from what cannot be derived:

• •Y appears in no dependency at all, so nothing determines it — it belongs to every key
• •T appears only on the left-hand side, so nothing determines it either — it also belongs to every key

Now test each addition by closure:

• •{P,T,Y} → P→Q gives Q, T→R gives R, QR→S gives S — all six attributes
• •{Q,T,Y} → T→R gives R, QR→S gives S, S→P gives P — all six
• •{S,T,Y} → S→P gives P, P→Q gives Q, T→R gives R — all six
• •{R,T,Y} → R is already implied by T and nothing further follows — not a key

Answer (d)

Why not others:
- (a) PT, QT and (b) PT, QT, ST — omit Y, which no dependency can ever produce
- (c) PTY, QTY, QRY — QRY closes to {Q,R,Y,S,P} but never reaches T

Key rule: Attributes that never appear on a right-hand side must be in every candidate key. Fixing them first turns the problem into a couple of small closure checks.

AI-generated — may contain errors