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Bogus rules
Disprove that if X and Y and Z are sets of attributes of a relation scheme R, and the fd X Y holds in R, then Y X also holds in R.
Disprove that if X, Y and Z are sets of attributes of a relation scheme R, and the fds X Y and Y Z hold in R, then Z X also holds in R.
Disprove that if X, Y and Z are sets of attributes of a relation scheme R, and the fds XY Z holds in R, then X YZ also holds in R.
Notes:
When coming up with inference rules one may “think” that a rule holds when in fact it does not. In order to show that a rule does not hold you must find (using your imagination) at least one instance in which the given functional dependencies hold and in which the “supposedly implied” functional dependencies do not hold.