Show the result of the sample query as it would apply to the database state in Figure $3\mathrm{.}6$

Query $4.$ Make a list of project numbers for projects that involve an employee whose last name is $$Smith$,$ either as a worker or as a manager of the department that controls the project.

SMITHS$($Essn$)\backslash$pi Ssn $(\backslash$sigma Lname$=$Smith$($EMPLOYEE$))$ SMITH$\_$WORKER$\_$PROJS $\backslash$pi Pno$($WORKS$\_$ON $*$ SMITHS$)$

MGRS $\backslash$pi Lname, Dnumber$($EMPLOYEE Ssn$=$Mgr$\_$ssnDEPARTMENT$)$ SMITH$\_$MANAGED$\_$DEPTS$($Dnum$)\backslash$pi Dnumber $(\backslash$sigma Lname$=$Smith$($MGRS$))$ SMITH$\_$MGR$\_$PROJS$($Pno$)\backslash$pi Pnumber$($SMITH$\_$MANAGED$\_$DEPTS $*$ PROJECT$)$ RESULT $($SMITH$\_$WORKER$\_$PROJS $\backslash$cup SMITH$\_$MGR$\_$PROJS$)$

In this query, we retrieved the project numbers for projects that involve an employee named Smith as a worker in SMITH$\_$WORKER$\_$PROJS. Then we retrieved the project numbers for projects that involve an employee named Smith as manager of the department that controls the project in SMITH$\_$MGR$\_$PROJS. Finally, we applied the UNION operation on SMITH$\_$WORKER$\_$PROJS and SMITH$\_$MGR$\_$PROJS. As a single in$-$line expression, this query becomes:

$\backslash$pi Pno $($WORKS$\_$ON Essn$=$Ssn$(\backslash$pi Ssn $(\backslash$sigma Lname$=$Smith$($EMPLOYEE$)))\backslash$cup $\backslash$pi Pno $((\backslash$pi Dnumber $(\backslash$sigma Lname$=$Smith$(\backslash$pi Lname, Dnumber$($EMPLOYEE$)))$ Ssn$=$Mgr$\_$ssnDEPARTMENT$))$ Dnumber$=$DnumPROJECT$)$