Consider following relation S (S1, S2, S3, E1, E2) and functional dependencies…

Explanation:

Find Candidate Key(s) -->

Given:

FD1: S1 → {S2, S3}
FD2: (E1, S3, S2) → S1
FD3: E2 → {S3, S2, E1}

So:
S1⁺ = {S1, S2, S3}
E2⁺ = {E2, S1, S2, S3, E1}
{E1, S2, S3}⁺ = {E1, S2, S3, S1}

E2 is a candidate key

Prime vs Non-prime Attributes

Prime attribute: E2
Non-prime attributes: S1, S2, S3, E1

1.CHECK BCNF

Condition: For every FD X → Y:
X is a superkey, Y can be anything

Check FD1:
S1 → S2, S3
S1 is not a superkey

So, it violates the condition of BCNF.

2.CHECK 3NF

Condition: For every FD X → Y:
X is a superkey OR
Y is prime

Check FD1:
S1 → S2, S3
S1 is not a superkey
S2, S3 are non-prime

So, it violates the condition of 3NF.

3.CHECK 2NF

Candidate key is single attribute (E2)
No partial dependency possible

Relation is in 2NF

Final Answer: 2NF