Consider the following relational database and give an expression in the relational algebra for each of the following queries:

employee$($ person$\_$name, street, city$)$

works $($person$\_$name, company$\_$name, salary$)$ company $($company$\_$name, city$)$

manages $($person$\_$name, manager$\_$name$)$

$($i$)$

$($ii$)$ find the company with smallest payroll.

$($iii$)$ Find the names and cities of residence of all employees who work for First bank corporation. $($iv$)$ Give all managers in the database a $10$ percent salary raise, unless the salary would be greater

than Rs$.100,000.$ In such cases give only a $3$ percent raise.