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+14 votes

The following functional dependencies are given:

$ AB\rightarrow CD,AF\rightarrow D,DE\rightarrow F,$$C\rightarrow G,F\rightarrow E,G\rightarrow A $

Which one of the following options is false?

  1. $ \left \{ CF \right \}^{*}=\left \{ ACDEFG \right \}$
  2. $ \left \{ BG \right \}^{*}=\left \{ ABCDG \right \}$
  3. $ \left \{ AF \right \}^{*}=\left \{ ACDEFG \right \}$
  4. $ \left \{ AB \right \}^{*}=\left \{ ABCDG \right \}$
asked in Databases by Active (3.7k points) | 1.5k views

from option D $\left \{ AB \right \}^{*}=\left \{ ABCDG \right \}$ the attribute $F$ has been removed it used to be $\left \{ ABCDFG \right \}$

this was done to let option C be the distinct one from all others.

2 Answers

+22 votes
Best answer

$\left \{ AF \right \}$*$ =\left \{ AFDE \right \}.$

Hence, option C is wrong.

answered by Boss (11.5k points)
edited by
yes. But what about {AB}*?
{AB}* are also looks correct. it is {ABCDG}

F cannot be derived from AB.
Yes. It might be a typo in the question. I removed F to make it correct.
+7 votes
All options correct except c option.
(a) (CF)*= {CFGADE} = {ACDEFG}

(b) (BG)*= {BGACD} = {ABCDG}

(d) (AB)*= {ABCDG}

but in (c) option, (AF)*={AFDE}
so option c is false.
answered by Junior (657 points)

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