(Solved): 1. [12pts] Solve the following normalization questions. a. Consider the relation \( \mathrm{R}=\{\ ...

1. [12pts] Solve the following normalization questions. a. Consider the relation \( \mathrm{R}=\{\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}, \mathrm{G}, \mathrm{H}, \mathrm{I}, \mathrm{J}\} \) and functional dependencies - \( \{\mathrm{A}, \mathrm{B}\} \rightarrow\{\mathrm{C}\} \) - \( \{A\} \rightarrow\{D, E\} \) - \( \{B\} \rightarrow\{F\} \) - \( \{\mathrm{F}\} \rightarrow\{\mathrm{G}, \mathrm{H}\} \) - \( \{D\} \rightarrow\{I, J\} \) What is the key for R? Decompose R into 2NF and then 3NF relations. b. Consider a relation \( \mathrm{R}=\{\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\} \) with the following dependencies. - \( \{\mathrm{A}, \mathrm{B}\} \rightarrow\{\mathrm{C}\} \) - \( \{\mathrm{C}, \mathrm{D}\} \rightarrow\{\mathrm{E}\} \) - \( \{D, E\} \rightarrow\{B\} \) Is \( \mathrm{AB} \) a candidate key of \( \mathrm{R} \) ? What about ABD? Explain your answer. c. Consider the relation \( \mathrm{R} \), which has attributes that hold schedules of courses and sections at a university; - \( \{ \) Course_no \( \rightarrow \) Ooffering_dept, Credit_hours, Course_level\} - Course_no, Sec_no, Semester, Year\} \( \rightarrow\{ \) Days_hours, Room_no, No_of_students, Instructor_ssn - \{Room_no, Days_hours, Semester, Year\} \( \rightarrow \) Instructor_ssn, Course_no, Sec_no Try to determine which sets of attributes form keys of R. How would you normalize this relation? d. Consider the following relation: - Carid \( \rightarrow \) Sale_date - Option_type \( \rightarrow \) Option_listprice - Carid, Option_type \( \rightarrow \) Option_discountedprice Argue using the generalized definition of the \( 3 \mathrm{NF} \) that this relation is not in \( 3 \mathrm{NF} \). Then argue from your knowledge of \( 2 \mathrm{NF} \), why it is not even in \( 2 \mathrm{NF} \).