edited by
1,802 views
4 votes
4 votes

Given the following functional dependencies

$\left\{X \rightarrow W, X \rightarrow Y, Y \rightarrow Z, Z \rightarrow PQ\right\}$

Consider the $FD$ set implied using above $FD$ set.

Implied $FD$ set = $\left\{X \rightarrow Z, X \rightarrow WY, X \rightarrow WZ, X \rightarrow YQ, Y \rightarrow P \right\}$

The number of functional dependencies in implied $FD$ set are invalid are ______________.

edited by

2 Answers

Best answer
6 votes
6 votes

All fds are valid x->y and y->z apply transitivity x->z

..x->y and x->w apply union rule x->wy  

X->z and x->w union rule gives x->wz

X-y and y->pq( transitivity)

Y->p decompisition rule

So x->yq

 Y -> z and Z->p  so y->p using transitivity

So ans is 0

edited by
0 votes
0 votes
All are valid

X→Z, by means of transitivity { x->y and y->z apply transitivity x->z }

X→WY, by means of union {x->y and x->w}

X→WZ, by means of union {x->z and x->w }

X→YQ, by means of transitivity and union {x-y and y->pq or (y->p and y-q) }

Y→P by means of transitivity

Related questions

6 votes
6 votes
5 answers
2
2 votes
2 votes
0 answers
3
1 votes
1 votes
0 answers
4
zeeshanmohnavi asked Jan 5, 2019
424 views
Can someone explain the paragraph marked based on relation $r$ given in Figure 7.2?Reference: Database System Concepts by Silberschatz, Korth, Sudarshan 4th Edition. ​�...