Use WHERE NOT EXISTS and Outer Joins
For all universal Programmes:
SELECT * FROM Programme
WHERE NOT EXISTS (SELECT * FROM 
                  (Participation NATURAL JOIN Programme) LEFT JOIN Employee
                      USING (Eid,Department) 
                  WHERE Employee.Eid IS NULL)
This should be fairly easy to explain - selects all programs where the is no employee not participating
For all enthusiatic employees:
SELECT * FROM Employee
WHERE NOT EXISTS (SELECT * FROM 
                  Employee LEFT JOIN Participation 
                      USING (Eid,department) 
                  WHERE Participation.Eid IS NULL)
Again - selects all employyes where there are no programs in the same department in which that employee is not participating.
This may look familiar if you are familiar with formal logic at all - universal quantification is generally defined in terms of negated existential qualification