database normalisation

Question

consider:

T1: {A11, A12, A13} - key is A11
T2: {A21, A22, A11} - key is A21
T3: {A21, A23} - key is {A21 A23}

T1, T2, T3 all are in which normal form?

a) 2nf

b) 3nf

c) BCNF

FUNCTIONAL DEPENDENCIES ARE NOT MENTIONED. SO, PLEASE EXPLAIN HOW TO CHECK NORMAL FORM FOR THE RELATION?

Comments

i think BCNF

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@Red_devil

HOW?

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only dependencies given are

A11->A12,A13

A21->A22,A11

SO A21->A22,A11,A12,A13 -(I)

now T3 in in BCNF because we dont get any dependencies between A21,A23;

same can be said about T2 BECAUSE WE DID NOT GET ANY DEPENDENCIES BETWEEN A22,A11;

AND SAME FOR T1,

what is the answer given ?? @iarnav

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@Red_devil

In  case of T2: Prime attribute A11 is on RHS as well

Then how it would be BCNF?

I think it should be in 3NF

 

Tell me if I am wrong. Thanks

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  @Ashwin Kulkarni   in T2 ONLY A21->A11,A22 IS GIVEN AND I DONT THINK THAT ANY OTHER DEPENDENCIES ARE PRESENT IN IT

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Ohh got it. i was thinking differently. yes this will be in BCNF.

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ans is BCNF

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@Red_devil

please tell how do you take/ assume the functional dependencies in a simple way with example?

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a key will always functionally determine the other attributes in its schema,actually its more difficult to construct the key from the list of FDs via closure.Here its straightforward.

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without giving FD's of relation it may be true A_{11}->A_{12}

A_{12}->A_{13}

A_{11}->A_{13}

it will be only in 2NF .is it possible or not???