The following relation satisfies FD C→AB.A B C1 2 11 2 22 2 3Question 3Select one:TrueFalse

To determine if the functional dependency (FD) C → AB is satisfied by the given relation, we need to examine the data that corresponds to this FD and check if, for every unique value of C, the combination of A and B remains the same.

Break Down the Problem

1. Identify the unique values of C from the given relation.
2. For each unique value of C, identify the corresponding values of A and B.
3. Check if the A and B values are consistent for each unique C value.

Relevant Concepts

• A functional dependency X → Y holds if, for every unique value of X in a relation, there is a unique corresponding value of Y.

Analysis and Detail

From the provided table, we have:

1. Unique Values of C: 11, 22, and 2.
2. Corresponding A, B values:
   • For C = 11, we have A = 1, B = 2.
   • For C = 22, we have A = 2, B = 2.
   • For C = 2, we have A = 2, B = 3.

Verify and Summarize

• For C = 11, (A, B) = (1, 2).
• For C = 22, (A, B) = (2, 2).
• For C = 2, (A, B) = (2, 3).

Since for the unique value of C = 2, we have two different pairs of (A, B): (2, 2) for C = 22 and (2, 3) for C = 2, it violates the condition for functional dependency. Specifically, C can map to two different combinations of values A and B.

Final Answer

False - The functional dependency C → AB is not satisfied by the given relation because the same C (in this case, C = 2) does not yield a unique pair (A, B).