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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. $\left \{ AB \right \}^{*}=\left \{ ABCDG \right \}$
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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.

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

Hence, option C is wrong.

edited
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{AB}* are also looks correct. it is {ABCDG}

F cannot be derived from AB.
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Yes. It might be a typo in the question. I removed F to make it correct.
All options correct except c option.

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

(d) (AB)*= {ABCDG}

but in (c) option, (AF)*={AFDE}
so option c is false.