UGC NET Computer Science Database Management Systems Previous Year Questions (PYQs)

Goal: Find a set of attributes whose closure covers all attributes of R = {A, B, C, D, E}.

Check (1) CD⁺:
From C → F we get F. D gives nothing further. So CD⁺ = {C, D, F}.
Missing A, B, E ⇒ not a key.

Check (2) EC⁺:
Start {E, C}. Using E → A ⇒ add A. Using A → B ⇒ add B. Using EC → D ⇒ add D.
Therefore EC⁺ = {E, C, A, B, D} = {A, B, C, D, E}. Covers all attributes of R ⇒ key.

Check (3) AE⁺:
A → B gives B; E → A adds nothing new. No way to reach C or D ⇒ not a key.

Check (4) AC⁺:
A → B gives B; C → F gives F. No E or D ⇒ not a key.

Answer: (2) EC

Note: F is outside R, so while C → F is valid, a key must cover only attributes of R. EC⁺ covers {A, B, C, D, E}.