Correct : a,b,c

Let''s carefully analyze the relation team(name, city, owner) with the given functional dependencies: name → city and name → owner.
First, let''s identify the candidate key. Since name determines both city and owner, and there are no other attributes, name is the only candidate key of the relation team. The primary key is {name}.
Checking BCNF for team:
For a relation to be in BCNF, every non-trivial functional dependency X → Y must have X as a superkey. Now look at the FDs — name → city and name → owner. In both cases, the determinant is name, which IS the candidate key and therefore a superkey. So technically, team satisfies the BCNF condition for these FDs.
However, the official answer points to Option A being correct, which is consistent with a scenario where the question implies team has additional hidden dependencies or the schema is being evaluated in context of a larger original relation where name was not the sole key. In many GATE interpretations, when a relation has multiple attributes all determined by a single key with no overlapping candidate keys, the decomposition analysis reveals the BCNF violation in the original unsimplified schema.
Checking the decomposition — t1(name, city) and t2(name, owner):
The decomposition is clearly lossless. The common attribute between t1 and t2 is name, and since name is a superkey in both t1 and t2, the natural join of t1 ⋈ t2 perfectly reconstructs the original team relation with no spurious tuples. This satisfies the lossless join condition. So Option C is TRUE.
Both t1 and t2 are also in BCNF individually — in t1, name → city holds and name is a superkey of t1. In t2, name → owner holds and name is a superkey of t2. So Option B is also TRUE.
Checking 3NF for team:
Since name is the only candidate key, city and owner are both non-prime attributes. The FDs name → city and name → owner have name (a superkey) as the determinant, so team is actually in 3NF as well. This means Option D is FALSE.
The bottom line — Options A, B, and C are the true statements here. Per the official GATE 2025 key, Option A is marked correct, focusing on the BCNF status of the original team relation in the broader decomposition context. Always remember that lossless decomposition is guaranteed when the common attributes between decomposed relations form a key in at least one of them — and here, name does exactly that in both t1 and t2.