Which of the following statement is correct, according to the following instance of the relational schema R(X, Y, Z)?

X	Y	Z
1	1	a
1	1	a
2	1	b
3	2	b

The correct answer is X → Y, X → Z 

Key PointsA functional dependency, denoted X → Y, refers to a relationship between two sets of attributes. If X → Y, this means that for all tuples in a relation, if two tuples have the same value for the set of attributes X, they must also have the same value for the set of attributes Y. Similarly, for Y → X, if two tuples have the same Y value, they must have the same X value.

Let's analyze the four options:

• X → Y, Z → X:  X is functionally dependent on Y because it is uniquely identify Y value but Z does not hold true because Z is not functionally dependent on X. so it is incorrect .
• Y → Z, Z → X: Y does not determine Z uniquely so it is also incorrect.
• X → Y, X → Z: X is functionally dependent on Y because it is uniquely identify Y value and X is functionally dependent on Z because it is uniquely identify Z value. So, both functional dependency are correct.
• Y → X, X → Z: Y does not determine X uniquely so it is also incorrect.

So, Correct answer is X → Y, X → Z