F1, F2, F3 are FD sets with FDs

Question

Isn't F1 covering F3 and F3 covering F1

Answer 1

F1: P->Q,Q->R

F2:P->Q,P->R

F3:P->Q,PQ->R

1) F1 and F3

F1 is covering F3 but F3 is not covering F1

F1: P->Q,Q->R

F3:P->Q,PQ->R

Q->R is not covered by F3

so F1 is not equivalent to F3

2)F1 and F2 are aslo not equivalent because P->R is not covered

3)F2 and F3 are equivalent

F2:P->Q,P->R

F3:P->Q,PQ->R

P->Q and P->R are covered by F3 

P->Q and PQ-R are covered by F2

so option B is correct

Comments

Hi Sandip Shaw

But , isn't PQ -> R means Q -> R already covered ?

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if you take Q from F1 and try to find the closure of Q the there is no production in F3 that can derive R

if you have production like Q->P and P->R

then you can say Q->R is covered

But here if you take Q only then how will you get PQ.if get PQ the only you can derive R.

Answer 2

No f3 is not covering f1 because in f1 Q->R bt in f3 this FD does not implies