A relation R(ABCDE) with FD set f = {A -> BC, C -> DE, D -> E} and the decomposition d = { R1(ABCD), R2(DE)}. Is this decomposition dependency preserving?

Question

The answer given is YES. But how is the dependency C -> DE preserved in this decomposition?

Answer 1

Yes its dependency preserving ,

from R1 we get  : A-> BCD and  C->D

       and R2 : D->E

now see , C->D amd D->E so we can say C->DE

So all dependency are preserved .

Comments

for dependency C--->DE --------------- 1 we have dependecy D--->E, now replace E with D in --------------- 1, we get C-------->DD means C---------->D. hence C------->D preserve in R1(ABCD) ?? am i right???

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What has explained is pseudo transitivity rule , and yes you're right.