Question

Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values.

F = {CH → G, A → BC, B → CFH, E → A, F → EG} is a set of functional dependencies (FDs) so that F⁺ is exactly the set of FDs that hold for R.

How many candidate keys does the relation R have?

1. 3
2. 4
3. 5
4. 6

Answer 1

Correct Answer - Option 2 : 4

The correct answer is “option 2”.

CONCEPT:

A set of attributes that uniquely identify tuples in a table is called the Candidate key.

It is a super key with no repeated attributes.

A table can have multiple candidate keys but only one primary key.

The primary key can be selected from the candidate keys.

Candidate keys may have multiple attributes.

A functional dependency is a relationship or dependency that exists between two attributes.

Closure means the complete set of all possible attributes that can be functionally derived from the functional dependencies.

Closure of C is denoted by C+.

EXPLANATION

According to the given dependencies,

CH → G

A → BC

B → CFH

E → A

F → EG

Since D is not part of any functional dependency so it can be a candidate key or maybe part of a candidate key.

To find more candidate keys add A, B, C, D, E, G, and H to D & find its closure:

(AD)⁺ = {ABCDEFGH}

(BD)⁺ = {ABCDEFGH}

(CD)⁺ = {CD}

(ED)⁺ = {ABCDEFGH}

(FD)⁺ = {ABCDEFGH}

(GD)⁺ = {GD}

(HD)⁺ = {HD}

Since AD, BD, ED and FD gives all attributes, so they are candidate keys.

Hence, the correct answer is “option 2”.