Consider the following schema of an administrative database for college personnel:

PROFESSOR$($SSN$,$ FNAME, LNAME, RANK, SALARY$)$

DEPARTMENT$($NAME$,$ OFFICE, PHONE, CHAIRID$)$

MEMBER$($DEPT NAME, PROF ID$)$

Primary keys are underlined in the schema definition. Foreign keys are as followConsider the following schema of an administrative database for college personnel:

PROFESSOR$($SSN$,$ FNAME, LNAME, RANK, SALARY$)$

DEPARTMENT$($NAME$,$ OFFICE, PHONE, CHAIRID$)$

MEMBER$($DEPT NAME, PROF ID$)$

Primary keys are underlined in the schema definition. Foreign keys are as follow:

Write the following queries in Relational Algebra.

$($a$)$ Retrieve full name $($first and last$)$ and rank of each professor who earns more than $40000$ dollars in

salary.

$($b$)$ Retrieve full name $($first and last$)$ of all professors who are members of the department named

MATH.

$($c$)$ Retrieve full name $($first and last$)$ of all professors who serve as department chair.

$($d$)$ Retrieve the salary of all professors who are members of more than one department.

Database is at top and in question