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.2, Problem 5E
Program Plan Intro
To show that if the professor Narcissus claims is correct or not.
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Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}. Find the reflexive closure of R
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Match each of the following relations on S = {the set of all people in the US} with the correct category. Your answer should include all properties that apply to the relation.
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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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- Given: Relation R = {(a,a), (a.b), (b,a). (b,b). (c,c)} and Set S = {a, b, c} Complete Relation R to be Transitive with Set Sarrow_forwardConsider the following set F of functional dependencies on the relation schema R = (A, B, C, D, E, G,H): A→ D AB→ DE BD→ A AC→ G a) Prove ABCH and BCDH are candidate keys of R. b) Give a lossless BCNF decomposition of R based on the set of functional dependencies (No need to compute the closure). Does the decomposition preserve dependencies? Why or why not? c) Given the following canonical cover: A->D AB->E BD->A AC->G Give a lossless dependency preserving 3NF decomposition of R accordingly. Again, no need to compute the closure.arrow_forwardConsider the following set F of functional dependencies on the relation schema(A, B, C, D, E, G):A → BCDBC → DEB → DD → A Prove (using Armstrong’s axioms) that AG is a superkey.arrow_forward
- Consider the relation R = {(1,3), (3,1), (2, 3), (3, 3), (3, 4), (4, 4), (4, 1)} on set {1, 2, 3, 4}. Find the reflexive closure of R.arrow_forwardPlease give step by step solution so i can fully understand. I a unsure how to go about solving this. Thank you in advance for your help! Question: Find at least 5 candidate key for the given relation by closureR(A,B,C,D,E,F)AB->CC->DD->BEE->FF->Aarrow_forwardConsider the relation ? = {(?, ?), (?, ?), (?, ?), (?, ?)} on the set {?, ?, ?, ?}. a. Find the reflexive closure of ?. b. Find the symmetric closure of ?. c. Find the transitive closure of ?.arrow_forward
- Consider the relation R = {(1,3), (3,1), (2, 3), (3, 3), (3, 4), (4, 4), (4, 1)} on set {1, 2, 3, 4}. Find the transitive closure of R.arrow_forwardConsider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.. Find the symmetric closure of R.arrow_forwardGiven set A={1,2,3,4,5} and let R and S be a binary relation on set A. ? = {(?, ?) ? ??? | ?|? } ??? ? = {(2,1), (2,3), (3,4), (3,5), (4,5)} a.) Evaluate the Domain and Range of SoR. b.) Evaluate (???) −1 ??? ??? ̅̅̅̅̅.arrow_forward
- Consider the relation R={(1,2),(2,1),(2,3),(3,4),(4,1)} on {1,2,3,4} Please solve 4,5,6arrow_forwardWe studied different properties of relations like reflexive, symmetric, antisymmetric, transitive. Please provide one example relation each for each property of the relation. Try to come up with original examples which can be seen practically. (Example, Reflexive relation R = {(a, b) | a and b share same birthday}, Symmetric relation R = {(a, b) | a and b are friends}, Antisymmetric relation R = {(a, b) | a is instructor of b}, Transitive relation R = {(a, c) | a is sibling of b, b is sibling of c, then a is sibling of c}arrow_forward4. _______ allow us to identify uniquely a tuple in the relation. a. Superkey b. Domain c. Attribute d. Schemaarrow_forward
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