HW4 Solution

# HW4 Solution - Database Management Systems(CIS 4301(Spring...

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Database Management Systems (CIS 4301) (Spring 2008) Instructor: Dr. Markus Schneider TAs: Ganesh Viswanathan Wenjie Yuan Homework 4 Solution Name: UFID: Email Address: Pledge (Must be signed according to UF Honor Code) On my honor, I have neither given nor received unauthorized aid in doing this assignment. _______________________________________________Signature For scoring use only: Maximum Received Exercise 1 16 Exercise 2 24 Exercise 3.1 15 Exercise 3.2 15 Exercise 3.3 30 Total 100

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Exercise 1 (Knowledge Questions) [16 points] Answer the following questions. 1. What is “functional” about functional dependencies? [2 points] Let r be the relation schema of a relation R, and let A, B R. B is functionally dependent on A, or A determines B functionally (uniquely), written A B if, and only if, to each value in A exactly one value in B belongs: A B t1, t2 R : t1[A] = t2[A] t1[B] = t2[B] for all possible relations R over r. We can see that in principle, there is a function A B that produces a set of value B according to a set of value A. This is “functional” about function dependencies. 2. What are Armstrong's Axioms for reasoning with a set of functional dependencies? [3 points] Let R be a relation schema, F a set of FDs and A, B, C R. The following inference rules are used to compute F + (Armstrong’s axioms): reflexivity rule: Let B A. Then always A B (special case: A A) holds. augmentation rule: If A B holds, then also A C B C holds. transitivity rule: If A B and B C holds, then also A C holds. 3. What are the goals of designing a good relation schema? [3 points] Solution: avoidance of redundancy and anomalies avoidance of information loss 4. What is meant by the closure of a set of functional dependencies? [2 points] F + is called the closure of F, means F + is the set of all FDs that can be logically implied from the FDs in F. 5. What is the difference between a key and a super key? [2 points] The difference between a key and a superkey is that a key has to be minimal; that is , if we have a key K={A1, A2, …,An} of R, then k-{Ai} is not a key of R for any Ai K.
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