Extraneous Attribute

Question

Let FD: AB-->C  , A-->C .Is B extraneous ?if yes, then how can we determine B.

Answer 1

B is  useless here , it could even have been ABDFRGTYUILOP-->C , then  BDFRGTYUILOP ,all these attributes are useless since A alone can determine C  , so u r left only with the functional dependency A-->C , as far as determining B is concerned , it is a prime attribute , since AB is a candidate key here . so in the given relation schema R(ABC) , you have only 1 functional dependency A-->C and AB is candidate key .

Answer 2

AB-->C

A-->C

2ND FUNCTIONAL DEPENDENCY SHOWS THAT 'A' ALONE CAN DERIVE C. SO IN 1ST FD B IS EXTRANEOUS . BECAUSE HERE A AND B TOGETHER DERIVING C. THIS IMPLIES THAT B IS NOT REQUIRED TO DERIVE C.A ALONE CAN DERIVE IT.AND IF WE REMOVE B,  A CLOSURE WILL REMAINS THE SAME.