So I am currently learning functional dependencies and need help with this HW question...... ### Database Relation and Functional Dependencies#### Table Structure| A | B | C | Tuple# ||----|----|----|--------|| 10 | B1 | C1 | #1 || 10 | B2 | C2 | #2 || 11 | B4 | C1 | #3 || 12 | B3 | C4 | #4 || 13 | B1 | C1 | #5 || 14 | B3 | C4 | #6 |#### Questions**a. Which of the following dependencies may hold in the above relation? If the dependency cannot hold, explain why by specifying the tuples that cause the violation.**i. \( A \rightarrow B \) ii. \( B \rightarrow C \) iii. \( C \rightarrow B \) iv. \( B \rightarrow A \) v. \( C \rightarrow A \) **b. Does the above relation have a potential candidate key? Explain.**---In analyzing functional dependencies:- **\( A \rightarrow B \)**: Check if the same value of A maps to a unique value of B. For tuples #1 and #2 with A=10, B is different (B1, B2), causing a violation. - **\( B \rightarrow C \)**: Check if the same value of B maps to a unique value of C. There are no repetitions of B-values that map to different C-values, thus it may hold. - **\( C \rightarrow B \)**: Check if the same value of C maps to a unique value of B. For tuples #1 and #3 with C=C1, B is different (B1, B4), causing a violation. - **\( B \rightarrow A \)**: Check if the same value of B maps to a unique value of A. Multiple examples such as tuples #1 and #5 (B1 to A=10, 13) show violations. - **\( C \rightarrow A \)**: Check if the same value of C maps to a unique value of A. For tuples #1 and #3 with C=C1, A is different (10, 11), causing a violation.**Candidate Key Analysis**A candidate key should uniquely identify all tuples in the relation. Here, no single attribute is able to uniquely

Solution: Given, a) i. A->B. Cannot hold. Eg : Tuple 1 has 10->b1, and 2# has 10->b2. This is the violation ii. B->C. This holds true. Eg : b1->c1 and b3->c4. There are no violation case iii. C->B does not holds true. Eg : c1->b1 and c1->b4. This is the violation. iv. B->A does not holds true. Eg : b1->10 and b1->13. v. C->A does not holds true. Eg : There is violation of c1 tuple. c1->10, c1->11, c1->13 b) This table does have a primary key, (B,C) because there is a dependency from B->C. There will always be a unique relation from B->C.

Engineering

Computer Science

A 10 10 11 12 13 14 B C B1 C1 B2 C2 B4 C1 B3 C4 B1 C1 #5 B3 C4 #6 Tuple# #1 #2 #3 #4 . Which of the following dependencies may hold in the above relation? If the dependency cannot hold, explain why by specifying the tuples that causes th violation? į. A⇒B ii. B⇒C iii. C⇒B iv. B⇒A v. C⇒A . Does the above relation have a potential candidate key? Explain.

A 10 10 11 12 13 14 B C B1 C1 B2 C2 B4 C1 B3 C4 B1 C1 #5 B3 C4 #6 Tuple# #1 #2 #3 #4 . Which of the following dependencies may hold in the above relation? If the dependency cannot hold, explain why by specifying the tuples that causes th violation? į. A⇒B ii. B⇒C iii. C⇒B iv. B⇒A v. C⇒A . Does the above relation have a potential candidate key? Explain.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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