Consider a relational schema team(name, city, owner), with functional dependencies \name city,\ name owner\. The relation team is decomposed into two relations, t_1(name, city) and t_2(name, owner). Which of the following statement(s) is/are TRUE?

The relations t_1 and t_2 are in BCNF.

The decomposition constitutes a lossless join.

The relation team is NOT in BCNF.

The relations t_1 and t_2 are in BCNF.

The decomposition constitutes a lossless join.

The relation team is NOT in 3NF.

GATE CSE 2025 Session 1 Q47: Normal forms and lossless join for team(name, city, owner)

Consider a relational schema $team(name, city, owner)$ , with functional dependencies $\{name \to city,\ name \to owner\}$ .

The relation $team$ is decomposed into two relations, $t_1(name, city)$ and $t_2(name, owner)$ . Which of the following statement(s) is/are TRUE?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: B, C (official GATE 2025 final answer key)

Concept used: BCNF: every non-trivial FD has a superkey on the left. Lossless join: the common attributes are a key of one side.

First step: Find the key of team: name determines everything, so name is a key and every FD has a superkey on its left.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key