1. Prove by example the following relational algebra property: ((R))= (R) as long as contains the attributes in You may use the COMPANY schema or another other schemas of your choice. Figure 5.6 One possible database state for the COMPANY relational database schema. EMPLOYEE \begin{tabular}{|l|c|l|c|c|c|c|c|c|c|} \hline Fname & Minit & Lname & Ssn & Bdate & Address & Sex & Salary & Super_ssn & Dno \\ \hline John & B & Smith & 123456789 & 19650109 & 731 Fondren, Houston, TX & M & 30000 & 333445555 & 5 \\ \hline Franklin & T & Wong & 333445555 & 19551208 & 638 Voss, Houston, TX & M & 40000 & 888665555 & 5 \\ \hline Alicia & J & Zelaya & 999887777 & 19680119 & 3321 Castle, Spring, TX & F & 25000 & 987654321 & 4 \\ \hline Jennifer & S & Wallace & 987654321 & 19410620 & 291 Berry, Bellaire, TX & F & 43000 & 888665555 & 4 \\ \hline Ramesh & K & Narayan & 666884444 & 19620915 & 975 Fire Oak, Humble, TX & M & 38000 & 333445555 & 5 \\ \hline Joyce & A & English & 453453453 & 19720731 & 5631 Rice, Houston, TX & F & 25000 & 333445555 & 5 \\ \hline Ahmad & V & Jabbar & 987987987 & 19690329 & 980 Dallas, Houston, TX & M & 25000 & 987654321 & 4 \\ \hline James & E & Borg & 888665555 & 19371110 & 450 Stone, Houston, TX & M & 55000 & NULL & 1 \\ \hline \end{tabular} DEPARTMENT DEPT_LOCATIONS \begin{tabular}{|l|c|c|c|} \hline \multicolumn{1}{|c|}{ Dname } & Dnumber & Mgr_ssn & Mgr_start_date \\ \hline Research & 5 & 333445555 & 19880522 \\ \hline Administration & 4 & 987654321 & 19950101 \\ \hline Headquarters & 1 & 888665555 & 19810619 \\ \hline \end{tabular} \begin{tabular}{|c|l|} \hline Dnumber & Dlocation \\ \hline 1 & Houston \\ \hline 4 & Stafford \\ \hline 5 & Bellaire \\ \hline 5 & Sugarland \\ \hline 5 & Houston \\ \hline \end{tabular} WORKS_ON PROJECT \begin{tabular}{|c|c|c|} \hline Essn & Pno & Hours \\ \hline 123456789 & 1 & 32.5 \\ \hline 123456789 & 2 & 7.5 \\ \hline 666884444 & 3 & 40.0 \\ \hline 453453453 & 1 & 20.0 \\ \hline 453453453 & 2 & 20.0 \\ \hline 333445555 & 2 & 10.0 \\ \hline 333445555 & 3 & 10.0 \\ \hline 333445555 & 10 & 10.0 \\ \hline 333445555 & 20 & 10.0 \\ \hline 999887777 & 30 & 30.0 \\ \hline 999887777 & 10 & 10.0 \\ \hline 987987987 & 10 & 35.0 \\ \hline 987987987 & 30 & 5.0 \\ \hline 987654321 & 30 & 20.0 \\ \hline 987654321 & 20 & 15.0 \\ \hline 888665555 & 20 & NULL \\ \hline \end{tabular} \begin{tabular}{|l|c|l|c|} \hline \multicolumn{1}{|c|}{ Pname } & Pnumber & Plocation & Dnum \\ \hline ProductX & 1 & Bellaire & 5 \\ \hline ProductY & 2 & Sugarland & 5 \\ \hline ProductZ & 3 & Houston & 5 \\ \hline Computerization & 10 & Stafford & 4 \\ \hline Reorganization & 20 & Houston & 1 \\ \hline Newbenefits & 30 & Stafford & 4 \\ \hline \end{tabular} DEPENDENT \begin{tabular}{|l|l|c|c|l|} \hline Essn & Dependent_name & Sex & Bdate & Relationship \\ \hline 333445555 & Alice & F & 19860405 & Daughter \\ \hline 333445555 & Theodore & M & 19831025 & Son \\ \hline 333445555 & Joy & F & 19580503 & Spouse \\ \hline 987654321 & Abner & M & 19420228 & Spouse \\ \hline 123456789 & Michael & M & 19880104 & Son \\ \hline 123456789 & Alice & F & 19881230 & Daughter \\ \hline 123456789 & Elizabeth & F & 19670505 & Spouse \\ \hline \end{tabular}