Given the following relations containing cruise information:

Cruise $($cid: integer, from: string, to: string, distance: integer, departs: time, arrival: time$)$

Ship $($sid: integer, sname: string, cruisingrange: integer$)$

Certified $($eid: integer, sid: integer$)$

Employees $($eid: integer, ename: string, salary: real$)$

Note that the Employees relation describes captain and other kinds of employees as well; every captain is certified for some ship $($otherwise$,$ he$/$she would not qualify as a captain$),$ and only captains are certified to manage a cruise.

Write the following queries in TRC and DRC$.$ Note that some of these queries may not be expressible in relational calculus. For such queries, please explain why they cannot be expressed.

Find the names of captains certified for Viking ships.

Find the cruise that can be managed by every captain whose salary is more than $$100,000.$

Find the names of captains who can operate ships with a range greater than $5000$ miles but are not certified on any Viking ships.