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Consider two relations R1 and R2, with n, attributes A1, A2, A3,…….., An. The functional dependencies on R1 and A1 → A2, A2→ A3,…...An-1→ An and R2 are A1→ A2, A2→ A3, ……..An-1, An→ A1. Then highest normal forms of R1 and R2 are respectively,

(A) 1NF,BCNF

(B) 2NF,2NF

(C) 3NF,3NF

(D) None

1 Answer

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The functional dependencies on R1 are A1 → A2, A2→ A3,…...An-1→ An.

A1+={A1,A2,A3..An}

So candidate key for R1 is A1. It is not in 3 NF as all other attributes are transitively dependent on A1. As there is no partial dependency so the given relation is in 2NF form.

 The functional dependencies on R2 are A1→ A2, A2→ A3, ……..An-1, An→ A1.

As An→ A1 and An is not derived by any other attribute so the primary key is An . as An+={A1,A2,A3....An}

So partial dependencies doesnt exist here also Hence it is also in 2NF

So the ans is b
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