GATE CSE 2014 Set 1 | Question: 30

Question

Given the following two statements: 

S1: Every table with two single-valued attributes is in $\text{1NF, 2NF, 3NF}$ and $\text{BCNF}.$ 

S2: $AB \to C, D \to E, E \to C$ is a minimal cover for the set of functional dependencies $AB \to C, D \to E, AB \to E, E \to C$.

Which one of the following is CORRECT?

• A. S1 is TRUE and S2 is FALSE.
• B. Both S1 and S2 are TRUE.
• C. S1 is FALSE and S2 is TRUE.
• D. Both S1 and S2 are FALSE.

Comments

if single-valued not given then also statement 1 correct?As any relation with two attributes will always be in BCNF so it will also be in 1NF,2NF and 3NF

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@Abhishek Rauthan If single-valued not given then is it even in 1NF?

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Yes it would not be in 1 nf also so statement 1 would be false

Answer 1

(A) S1 is TRUE and S2 is FALSE.

A relation with $2$ attributes is always in BCNF

The two sets of functional dependencies are not the same. We can not derive $AB \to E$ from the $1^{\text{st}}$ set.

Comments

can not derive AD→E from the 1st set

just correct it : AB → E

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It's AB$\rightarrow E$ not AD $\rightarrow E$

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@learncp  , the table you assumed is wrong because Relational Table cannot contain duplicates . 

Answer 2

S1 is true bcoz if there are only 2 attributes then relation is always in bcnf.

let R(A B) possible cases are:

(1) {A->B } here A is cand key so BCNF

(2) {B->A}  here B is cand key so BCNF

(3) { A->B  B->A} here A and B both are cand key so BCNF

​​​​​​​(4) no non-trivial FD's here AB is cand key so BCNF

S2 is false bcoz minimal cover should be { D->E , AB->E , E->C }

so ans is A

Answer 3

Table with 2 single valued attributes will be in 1NF,

2NF because there can not be a partial key dependencies. Key can be 1 attribute or 2 attributes. If one is key then other can be dependent, if 2 attributes make key then it is trivial.

3NF, there is no question of Transitive dependencies.

BCNF, because if at all a dependency exists, the determinant will be a Key.

Answer 4

s1 is true and s2 is false.In s2 AB->E is not covered.