Assume a database with the schema:

ACTOR (name, age, address, nationality)

MOVIE(title, year, budget, director-name, studio)

APPEARS(name, title, salary)

Write the following questions in relational algebra:

(a) List the names and nationalities of actors that have appeared in any movie produced by studio 'MGM' in the year 2000. (b) List pairs of actors names that have appeared together in some movie. That is, ist pairs (namel,name2) whenever there is some movie ' such that both 'namel' and 'name2' appeared n movie m (c) List titles and budget of movies where at least two Australian actors have appeared. (d) List the names of actors that have never appeared in any movie produced by studio 'MGM. (e) List the names of actors that have never made more than 1,000,000 in a movie