Consider the table R with attributes A, B and C. The functional dependencies that hold on R are : A andrarr;B, C andrarr;AB. Which of the following statements is/are true? The decomposition of R into R1(C, A) and R2(A, B) is lossless. The decomposition of R into R1(A, B) and R2(B, C) is lossy.a)Only 1b)Only 2c)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer? - EduRev Computer Science Engineering (CSE) Question

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Consider the table R with attributes A, B and C. The functional dependencies that hold on R are : A → B, C → AB. Which of the following statements is/are true?

The decomposition of R into R₁(C, A) and R₂(A, B) is lossless.
The decomposition of R into R₁(A, B) and R₂(B, C) is lossy.

a)
Only 1
b)
Only 2
c)
Both 1 and 2
d)
Neither 1 nor 2

Correct answer is option 'C'. Can you explain this answer?

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Most Upvoted Answer

Consider the table R with attributes A, B and C. The functional depend...

→ B, B → C, and A → C.

This means that A uniquely determines B, B uniquely determines C, and A uniquely determines C.

For example, if we know the value of A for a tuple in R, we can determine the value of B and C for that same tuple. Similarly, if we know the value of B for a tuple in R, we can determine the value of C for that same tuple.

This set of functional dependencies also implies that there are no other functional dependencies that hold on R. For example, we cannot say that B determines A or C determines B.

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Consider the table R with attributes A, B and C. The functional depend...

Decomposition of R into R₁(C, A) and R₂(A, B) is lossless.
Because C → A, A → B, so C → AB can be derived and there is no loss.
Decomposition of R into R₁(A, B) and R₂(B, C) is lossy.
Because A → B, C → B are derived but we can't derive C → AB, so it is lossy.
So, option (3) is correct.

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Consider the table R with attributes A, B and C. The functional dependencies that hold on R are : A →B, C →AB. Which of the following statements is/are true? The decomposition of R into R1(C, A) and R2(A, B) is lossless. The decomposition of R into R1(A, B) and R2(B, C) is lossy.a)Only 1b)Only 2c)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?

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