Question

Let R(A,B,C,D,E) is a relational schema with the following functional

dependencies:

F={A->BC,CD->E,B->D,E->A}.List the candidate keys of R​

Answer 1

Answer:

its to difficult l dont know

Answer 2

Answer:

The candidate keys are A, E, CD, and BC

Explanation:

A -> BC, B -> D so A -> D so A -> DC -> E therefore A -> ABCDE

E -> A, A -> ABCDE, so E -> ABCDE

CD -> E, so CD -> ABCDE

B -> D, BC -> CD, so BC -> ABCDE

Attribute closure: A -> ABCDE

B -> BD

C -> C

D -> D

E -> ABCDE

AB -> ABCDE

AC -> ABCDE

AD -> ABCDE

AE -> ABCDE

BC -> ABCDE

BD -> BD

BE -> ABCDE

CD -> ABCDE

CE -> ABCDE

DE -> ABCDE

ABC -> ABCDE

ABD -> ABCDE

ABE -> ABCDE

ACD -> ABCDE

ACE -> ABCDE

ADE -> ABCDE

BCD -> ABCDE

BDE -> ABCDE

CDE -> ABCDE

ABCD -> ABCDE

ABCE -> ABCDE

ABDE -> ABCDE

ACDE -> ABCDE

BCDE -> ABCDE

The candidate keys are A, E, CD, and BC . Any combination of attributes that includes those is a superkey.