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+15 votes
1.5k views

Given the following relation instance.

                X      Y      Z 
                1      4      2 
                1      5      3 
                1      6      3 
                3      2      2

Which of the following functional dependencies are satisfied by the instance?

  1. XY → Z and Z → Y                                      
  2. YZ → X and Y → Z
  3. YZ → X and X → Z                                    
  4.  XZ → Y and Y → X

 

asked in Databases by Veteran (68.8k points)
edited by | 1.5k views

3 Answers

+24 votes
Best answer
(b)

if a->b then for each same value of a , b should be same,

we have to get the opposite of the defn i.e if no values of a are same then b need be same
answered by Loyal (3.4k points)
edited by
Yes. In (b) a is not repeating and so, FD trivially holds. In all other options, FD condition is easily violated.
+11 votes

Option B is correct.

a functional dependency A \rightarrow B is said to hold if for two tuples t1 and t2 . If for t1[A] = t2[A] then t1[Y] = t2[Y].

Here we can manually check for each option with the given instance and option B satisfies

answered by Veteran (12.1k points)
–2 votes
Ans: B YZ → X and Y → Z
answered by Boss (7.4k points)


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