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Canonical Cover Exercise
Let {A,B,C,D,E} be the attributes of R and let F={AB, ABC, DEC, EBCD}. Compute Fc.
Notes:
Following the algorithm of Figure 7.8 we perform the following steps:
1. Initially we cannot apply the union rule
2. We check whether B is extraneous in ABC.
From AB we deduce AAB by augmentation.
From AAB and ABC we deduce AC by transitivity.
We can thus replace ABC by AC without making F stronger.
3. We can now apply the union rule to replace AB and AC by ABC.
4. We now check whether D is extraneous in DEC.
From EBCD and the trivial BCDD we deduce ED by transitivity.
From ED we deduce EDE by augmentation.
From EDE and DEC we deduce EC by transitivity.
We can thus replace DEC by EC without making F stronger.
5. We can now apply the union rule to replace EC and EBCD by EBCD.
The resulting set is {ABC, EBCD}. It can not be reduced any further.