GATE IT 2007 | Question: 67

Question

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?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Comments

8 statements are given in question while there should be only 4.. Which 4 statements were there in original question

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$\text{Good READ on Multi-valued dependency(MVD):}$

https://www.geeksforgeeks.org/dbms/multivalued-dependency-mvd-in-dbms/

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if single valued holds then multi-valued also holds but if multi-value holds then single valued may or may NOT hold

Answer 1

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: $C$

Comments

@Lakshman Patel RJIT so if we ignore it completely it will be ok ?? i have seem questions from this topic in some test series that’s why i am worried.

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As we don't know what GATE can ask. It is rarely asked & most probably won't be asked. So it’s good to know the things.

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https://homepages.cwi.nl/~manegold/teaching/DBtech/slides/appC-8.pdf

Answer 2

Check answer to following question ->

http://dba.stackexchange.com/questions/123510/how-can-i-prove-disprove-if-a-%E2%86%A0-bc-and-a-%E2%86%92-b-then-a-%E2%86%92-c

Answer 3

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 4

We know that, if  x->y exist in a retation then x->->y must be exixt in that relationship. But if x->->y exists then x->y may or may not be exists in the relation.

Option 1: if A->->B and  A->->C then there are no guarantees that A->B & A->C (A->BC) exist. Then it is a invaild implication.

Option 2: if A->B and A->C then using union we can say that A->BC then A->->BC must exist. Then it is a vaild implication.

Option 3: if A->->BC exist then there are no guarantee about A->BC then A->B and A->C is invaid implication.

Option 4:  if A->BC exist then using decomposition or spiliting we can say that A->B abd A->C also exist. For exixtance of A->C, A->->C  also exixts. this is also valid implication.

Overall 2 implication are valid .Ans-C

Comments

is this method always be applicable

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Yes

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@souringuchait
This should be selected as best answer!

Answer 5

 

Every Functional Dependency is MutliDependency, but converse is not true.So,every rule of functional Dependency can apply to Multi Dependencies.

B is   (Union) and D is  (decomposition) are ensure the functional Dependencies so theyare also Mutli dependencies. Therefore 2 and 4 can hold the result.

Answer 6

Implication 1 (A →→ B and A →→ C, then A → BC) is valid.

• If A multidetermines both B and C independently, it implies that for a given value of A, B and C can have multiple, independent values. This effectively means A functionally determines the combined set of values for B and C.
  ans is B