1. Consider the following relational schema for airline flights. Primary keys are un- derlined; foreign keys are implied by identically named attributes. FLIGHTS (Flnum, Origin, Destination, Distance, Departure, Arrival) AIRCRAFT (Ald, Range, Manufacturer) CERTIFIED (Eld, Ald) EMPLOYEES (Eld, Ename, Salary) We are told that the EMPLOYEES relation contains not only pilots but also other kinds of employees. However, only pilots are certified to fly and each pilot is certified for at least one aircraft. The CERTIFIED relation lists, for each pilot, which aircraft(s) he / she is certified for. In FLIGHTS, the attributes are the flight number, the three- letter codes for the origin and destination airports, the distance between those two airports, and finally the departure and arrival times. In the AIRCRAFT relation, range represents the maximum distance (in miles) the aircraft can fly non-stop; manufacturer is the company that has made the aircraft; below, we use the expression Boeing aircraft to mean an aircraft whose manufacturer is the Boeing company. Write the following queries in relational algebra. You may break up a complex expression by assigning subexpressions to new relation names. You may use non-relational operators only when relational operators are inad- equate; explain informally why it is necessary to go beyond relational algebra. $1. Find the names of pilots certified for some (i.e., at least one) Boeing aircraft. 82. List the manufacturers of all aircrafts we know about (in the Aircraft relation). $3. Find the Alds of all aircrafts that can be used on non-stop flights from IAD (Washington, D.C.) to DEL (New Delhi). $4. Identify the flights (by their Flnum) that can be piloted by every pilot whose salary is less than $80,000. $5. Find the Elds of employee(s) who earn the highest salary. Hint: Focus on those who don't. $6. Find the Elds of employees who are certified for exactly two aircrafts. Hint: Can you find those certified for two or more and those for three or more? 87. Find the total amount paid to pilots as salaries