GATE CSE 2012 | Question: 2

Question

Which of the following is TRUE?

• A. Every relation in $\text{3NF}$ is also in $\text{BCNF}$
• B. A relation $\text{R}$ is in $\text{3NF}$ if every non-prime attribute of $\text{R}$ is fully functionally dependent on every key of $R$
• C. Every relation in $\text{BCNF}$ is also in $\text{3NF}$
• D. No relation can be in both $\text{BCNF}$ and $\text{3NF}$

Comments

All BCNF is in 3NF
All 3NF is in 2NF
All 2NF is in 1NF

---

OPTION - C . bcs if x(super key ) -> y(prime / not prime ) then 3nf satisfy. so if BCNF satisfies then 3nf also satisfy.

OPTION - B satisfy for 2nf , not for 3nf .

---

Option C is correct

Answer 1

Option A  is false as Every higher normal form contain lower normal form

Option B Due to non prime word it is false there should be prime 

Option C is True Infered from option A  that is  Every higher normal form contain lower normal form

Option D is false 

Answer 2

COMMENT BELOW IF YOU HAVE ANY DOUBT

Answer 3

A ) It is false since for 3NF in a FD say X->A(either X needs to be SK or A a prime attribute) while for BCNF all we need is for X to be a SK.

So for a case were X is not a SK and A is a prime attribute this statement is incorrect.

B ) Definition of 3NF : A relation R is in 3NF if every Non-Prime Attribute is not transitively dependent on ever CK of R

Hence this is false too.

C) From tthe definiton of BCNF, Every 3NF is also in BCNF

Hence this statement is Correct

D) Contradictory to the definiton of BCNF

Option C is True, Rest False.