Consider a relational schema for storing information related to movies:

Actor$($name$,$ YofB, country$\_$of$\_$birth, bio, gender$)$

Director$($name$,$ YofB, country$\_$of$\_$birth, bio, gender$)$

Producer$($name$,$ YofB, country$\_$of$\_$birth, bio, gender$)$

Crew$($name$,$ YofB, country$\_$of$\_$birth, bio, $)$

Country$($code$,$ country$\_$name, description$)$

Movie$($title$,$ release year, genre, budget, cost, gross$\_$earnings$)$

DirectorMovie$($d$\_$name, d$\_$YofB, $m$ title, $m\_$year$)$

ActorMovie$($a$\_$name, a YofB, $m$ title, $m$ year$)$

CrewMovie$($c$\_$name, c$\_$YofB, m$\_$title, $m\_$year$)$

ProducerMovie$($p$\_$name, p$\_$YofB, $m\_$title, $m$ year, p$\_$type$)$

Foreign key constraints:

Actor$[$country$\_$of$\_$birth$]$ sube Country$[$code$]$

Director$[$country$\_$of$\_$birth$]$ sube Country$[$code$]$

Producer$[$country$\_$of$\_$birth$]$ sube Country$[$code$]$

DirectorMovie$[$d$\_$name, d$\_$YofB$]$ sube Director$[$name$,$ YofB$]$

DirectorMovie$[$m$\_$title, m$\_$year$]$ sube Movie$[$name$,$ release$\_$year$]$

ActorMovie$[$a$\_$name, a$\_$YofB$]$ sube Actor$[$name$,$ YofB$]$

ActorMovie$[$m$\_$title, m$\_$year$]$ sube Movie$[$name$,$ release$\_$year$]$

ProducerMovie$[$p$\_$name, p$\_$YofB$]$ sube Producer$[$name$,$ YofB$]$

ProducerMovie$[$m$\_$title, m$\_$year$]$ sube Movie$[$name$,$ release$\_$year$]$

CrewMovie$[$c$\_$name, c$\_$YofB$]$ sube Crew$[$name$,$ YofB$]$

CrewMovie$[$m$\_$title, m$\_$year$]$ sube Movie$[$name$,$ release$\_$year$]$

Part $1.[30$ points$]$ Write Relational Algebra expressions for the following queries. Use only the

operators presented in class. Do not use extended Relational Algebra operators, e$.$g$.,$ grouping,

counting, etc.

a$.$ List the name and year of birth of all those who acted in at least two movies which they also

directed.

b$.$ List the name and year of birth of all directors who were younger than all the actors cast in the

movies they directed, at the time the movie was released. $($The persons returned by this query may

be associated with movies in other capacities as well, e$.$g$.,$ as actors, directors, executive

producers, etc. Person A is "younger" than person B is the age of person A is less or equal to the

age of person B$.)$

c$.$ List the name and year of birth of all producers who only produced in one type of movie, for

example only acted in comedies. $($The persons returned by this query may be associated with

movies in other capacities as well, e$.$g$.,$ as actors, directors, etc.$)$