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Consider the following implications relating to functional and multivalued dependencies given below, which may or may not be correct.

  1. if $A \rightarrow \rightarrow B$ and $A \rightarrow \rightarrow C$ then $A \rightarrow  BC$
  2. if $A \rightarrow B$ and $A \rightarrow  C$ then $A \rightarrow \rightarrow BC$
  3. if $A \rightarrow \rightarrow BC$ and $A \rightarrow  B$ then $A \rightarrow C$
  4. if $A \rightarrow BC$ and $A \rightarrow  B$ then $A \rightarrow \rightarrow C$

Exactly how many of the above implications are valid?

  1. $0$
  2. $1$
  3. $2$
  4. $3$
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3 Answers

Best answer
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a. If A → → B and A  → →C then A → BC . So FALSE
b. If A → B and A → C then A→ BC.   So   A → →BC    TRUE..
c. If A → → BC and A → B  here B is Subset of AB and (A intersection BC) is phi so
 A → B but not A → C so FALSE  (Coalescence rule )
d. If A → BC  then A → C   so  A → → C    TRUE
 if A → B then A → → B  holds but reverse not true.

Correct Answer: $C$

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Every FD is a MVD.

i.e suppose $x\rightarrow y$  $\Rightarrow$ $x\rightarrow \rightarrow y$

If y can be determined by x on y's single value then we can easily say x multi-determines y. as single value $\subseteq$ multiple value.

Now,

1. can't even possible.

2.  A -> BC which implies A -> -> BC. (true)

3. using given data we can't prove the then part.

4. given FDs are A->B & A->C, so using this we can say A->->C.(true)

here 2 implications are valid. i.e option C

Answer:

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