Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter B.3, Problem 3E
Program Plan Intro
To provide example, of binary relation, whose relational inverse is its functional inverse.
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To provide a transitive closure (exhaustive) query of prerequisites, we need to use a query that is _______, which is to say that it is defined in terms of itself.
The transitive closure of the relation prereq is a relation that contains all pairs (cid, pre) such that pre is a direct or indirect prerequisite of cid.
Consider a relation R(A,B,C,D,E) with functional dependencies AB→C, A→D, and D→E. (a) What are the keys for R?(b)What is the closure A, that is A+ ? What is the closure AB, that is (AC)+ ?
let R be a relation defined on the set z by aRb if a < b. What property/properties are violated?
A. Symmetric & transitive
B. Reflexive & Symmetric
C. Reflexive & Transitive
D. All three properties
Chapter B Solutions
Introduction to Algorithms
Ch. B.1 - Prob. 1ECh. B.1 - Prob. 2ECh. B.1 - Prob. 3ECh. B.1 - Prob. 4ECh. B.1 - Prob. 5ECh. B.1 - Prob. 6ECh. B.2 - Prob. 1ECh. B.2 - Prob. 2ECh. B.2 - Prob. 3ECh. B.2 - Prob. 4E
Ch. B.2 - Prob. 5ECh. B.3 - Prob. 1ECh. B.3 - Prob. 2ECh. B.3 - Prob. 3ECh. B.3 - Prob. 4ECh. B.4 - Prob. 1ECh. B.4 - Prob. 2ECh. B.4 - Prob. 3ECh. B.4 - Prob. 4ECh. B.4 - Prob. 5ECh. B.4 - Prob. 6ECh. B.5 - Prob. 1ECh. B.5 - Prob. 2ECh. B.5 - Prob. 3ECh. B.5 - Prob. 4ECh. B.5 - Prob. 5ECh. B.5 - Prob. 6ECh. B.5 - Prob. 7ECh. B - Prob. 1PCh. B - Prob. 2PCh. B - Prob. 3P
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- Consider the following set F of functional dependencies on the relation schema(A, B, C, D, E, G):A → BCDBC → DEB → DD → A Compute B+.arrow_forward. A relation R on a set S, defined as x R y if and only if y R x. This is an example of?a) reflexive relationb) symmetric relationc) transitive relationd) invalid relationarrow_forwardConsider the relation schema R (A, B, C, D, E, F, G, H) with the set of functional dependencies K = {A→B, B→DE, F→H, G→CE}. Determine all candidate keys of R in a systematic manner (do not use the Armstrong's Axioms) and explain how you determine them. Show each step.arrow_forward
- Determine whether the given relation is reflexive, symmetric, anti-symmetric and transitive (x, y)∈R if and only if y=x is less than and equal to x^2arrow_forwardConsider a relation schema R = (X, Y, Z) on which the following functionaldependencies hold: { XY → Z, Z → X }. Show that the schema R is not in BCNF(Boyce-Codd Normal Form) but it is in 3NF (Third Normal Form). Answer in detailarrow_forwardGive a set of FDs for the relation R (ABCD) with AB as primary key under which condition R is in 2NF but not in 3NF. Warning-Give correct answer , i will report and downvote youarrow_forward
- Consider the following set F of functional dependencies on the relation schema(A, B, C, D, E, G):A → BCDBC → DEB → DD → A Give a 3NF decomposition of the given schema based on a canonical cover.arrow_forwardConsider a functional dependency α → β on a relation schema R. In which of the following conditions, when satisfied, we can say for sure that α → β is not ntrivial?(a) α ∩β = ∅(b) α ∪β = α(c) α ⊂ β(d) β ⊆ α(e) none of the abovearrow_forwardConsider the Relation R4 = (A,C,B,D,E,F), with Functional Dependencies: A -> B, C -> D, E -> D. What is the Candidate Key for R4?arrow_forward
- Compute the closure of the following set F of functional dependencies for relation schema R = (A, B, C, D, E). A → BC CD → E B → D E → A List the candidate keys for R.arrow_forwardConsider the following proposed rule for functional dependencies: If α → β and γ → β, then α → γ. Prove that this rule is not sound by showing a relation r that satisfies α → β and γ → β, but does not satisfy α → γ.arrow_forwardConsider a relation r(A, B, C), with an index on attribute A. Give an example of a query that can be answered by using the index only, without looking at the tuples in the relation. (Query plans that use only the index, without accessing the actual relation, are called index-only plans.)arrow_forward
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