D1 Reasoning with dependencies 1. Prove that {AB → C,A → D,CD → EF} E AB → F holds using only the Armstrong Axioms. | | 2. Prove the soundness of the following inference rule directly from the definition of functional depen- dencies (without using any inference rules): if X →Y and YW → Z, then XW → Z. 3. Prove the soundness of the following inference rule for inclusion dependencies: if R[X] C S[Y] and S[Y] C T[Z], then R[X] CT[Z]. 4. Prove the soundness of the following inference rule if X » Y and XY → Z, then X → Z\ (XUY). 5. Prove that the following inference rule is not sound: if XW Y and XY Z, then X Z. ->
D1 Reasoning with dependencies 1. Prove that {AB → C,A → D,CD → EF} E AB → F holds using only the Armstrong Axioms. | | 2. Prove the soundness of the following inference rule directly from the definition of functional depen- dencies (without using any inference rules): if X →Y and YW → Z, then XW → Z. 3. Prove the soundness of the following inference rule for inclusion dependencies: if R[X] C S[Y] and S[Y] C T[Z], then R[X] CT[Z]. 4. Prove the soundness of the following inference rule if X » Y and XY → Z, then X → Z\ (XUY). 5. Prove that the following inference rule is not sound: if XW Y and XY Z, then X Z. ->
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![Description
The Professor S. Marty Pants, a recent faculty hire of the University, is convinced that they are the smartest
database person of all times. To impress people, the Professor often states problems that the Professor then
claims are almost impossible to solve and then shows how to solve them. Next, we will take a look at a few
of these problems from three categories:
D1 Reasoning with dependencies
1. Prove that {AB → C,A → D, CD → EF} = AB
→ F holds using only the Armstrong Axioms.
2. Prove the soundness of the following inference rule directly from the definition of functional depen-
dencies (without using any inference rules):
if X → Y and Yw → Z, then XW → Z.
3. Prove the soundness of the following inference rule for inclusion dependencies:
if R[X] C S[Y] and S[Y] C T[Z], then R[[X] C T[Z].
4. Prove the soundness of the following inference rule
if X » Y and XY → Z, then X →
Z \ (XUY).
5. Prove that the following inference rule is not sound:
if XW → Y and XY → Z, then X → Z.
HINT: Look for a counterexample by constructing a table in which XW → Y and XY → Z hold,
but X → Z does not hold.
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cdae1b3-511b-42a7-83bc-b26c890aa6cb%2Fd36c5e4a-5387-4fb7-b441-56f1519bbc00%2Frx57ffh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Description
The Professor S. Marty Pants, a recent faculty hire of the University, is convinced that they are the smartest
database person of all times. To impress people, the Professor often states problems that the Professor then
claims are almost impossible to solve and then shows how to solve them. Next, we will take a look at a few
of these problems from three categories:
D1 Reasoning with dependencies
1. Prove that {AB → C,A → D, CD → EF} = AB
→ F holds using only the Armstrong Axioms.
2. Prove the soundness of the following inference rule directly from the definition of functional depen-
dencies (without using any inference rules):
if X → Y and Yw → Z, then XW → Z.
3. Prove the soundness of the following inference rule for inclusion dependencies:
if R[X] C S[Y] and S[Y] C T[Z], then R[[X] C T[Z].
4. Prove the soundness of the following inference rule
if X » Y and XY → Z, then X →
Z \ (XUY).
5. Prove that the following inference rule is not sound:
if XW → Y and XY → Z, then X → Z.
HINT: Look for a counterexample by constructing a table in which XW → Y and XY → Z hold,
but X → Z does not hold.
1
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