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?
(b) is answer.
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.
Option B is correct.
a functional dependency 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
YZ->X and Y->Z. Here YZ uniquely determines X and Y uniquely determines Z.