Consider a relational schema \(π‘‘π‘’π‘Žπ‘š(π‘›π‘Žπ‘šπ‘’, 𝑐𝑖𝑑𝑦, π‘œπ‘€π‘›π‘’π‘Ÿ)\),…

GATE Β· 2025 Β· CS Β· Set 1 Β· Computer Science & IT

Consider a relational schema π‘‘π‘’π‘Žπ‘š(π‘›π‘Žπ‘šπ‘’,𝑐𝑖𝑑𝑦,π‘œπ‘€π‘›π‘’π‘Ÿ)π‘‘π‘’π‘Žπ‘š(π‘›π‘Žπ‘šπ‘’, 𝑐𝑖𝑑𝑦, π‘œπ‘€π‘›π‘’π‘Ÿ), with functional dependencies {π‘›π‘Žπ‘šπ‘’β†’π‘π‘–π‘‘π‘¦,π‘›π‘Žπ‘šπ‘’β†’π‘œπ‘€π‘›π‘’π‘Ÿ}\{π‘›π‘Žπ‘šπ‘’ β†’ 𝑐𝑖𝑑𝑦, π‘›π‘Žπ‘šπ‘’ β†’ π‘œπ‘€π‘›π‘’π‘Ÿ\}.

The relationΒ π‘‘π‘’π‘Žπ‘šπ‘‘π‘’π‘Žπ‘š is decomposed into two relations, 𝑑1(π‘›π‘Žπ‘šπ‘’,𝑐𝑖𝑑𝑦)𝑑1(π‘›π‘Žπ‘šπ‘’, 𝑐𝑖𝑑𝑦) and 𝑑2(π‘›π‘Žπ‘šπ‘’,π‘œπ‘€π‘›π‘’π‘Ÿ)𝑑2(π‘›π‘Žπ‘šπ‘’, π‘œπ‘€π‘›π‘’π‘Ÿ). Which of the following statement(s) is/are TRUE?

  1. A.

    The relationΒ π‘‘π‘’π‘Žπ‘šπ‘‘π‘’π‘Žπ‘š is NOT in BCNF.

  2. B.

    The relationsΒ t1t1 andΒ t2t2 are in BCNF.

  3. C.

    The decomposition constitutes a lossless join.

  4. D.

    The relationΒ π‘‘π‘’π‘Žπ‘šπ‘‘π‘’π‘Žπ‘š is NOT in 3NF.

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