The Database, whose relational scheme is given below, contains data regarding the Student Selection and Placement System.

OKUL $($OKKODU$,$ OKADI, KENT, ADRES$)$

OKULT$$R$($T$$RKODU$,$ T$$RADI$)$

KOL $($KOLKODU$,$ KOLADI$)$

T$$RKOL $($T$$RKODU$,$ KOLKODU$)$

OKULT$$R $($OKKODU$,$ T$$RKODU$,$ SIRNO$)$

OKULT$$RKOL $($OKKODU$,$ T$$RKODU$,$ KOLKODU$)$

$$N$$V $($NO$,$ADI$,$ADRES$)$

Y$$PROG $($Y$$PKODU$,$ Y$$PADI$,$NO$,$RS$$R$,$ KENT$)$

ADAY $($ADYNO$,$ ADI, SOYADI, OKKODU, T$$RKODU$,$ KOLKODU, KY$$PKODU$)$

TERC$$H $($ADYNO$,$ Y$$PKODU$,$ TRCSIR$)$

Brief explanations about the database are as follows.

$$ OKUL relationship includes the codes, names, cities and addresses of secondary schools.

$$ OKULT$$R$$ relationship includes the codes and names of school types $($general high school, science high school, trade high school, etc.$).$

$$ KOL relationship includes the codes and names of school branches $($mathematics$,$ Turkish$-$mathematics, accounting, etc.$).$

$$ T$$RKOL relationship includes data on which branches$/$branches can be found in which types of schools.

$$ OKULT$$R relationship shows the type or types of each school. Although most schools have a single type, some schools may have more than one type $($for example, both technical high school and industrial vocational high school$).$

$$ OKULT$$RKOL relationship shows which type of school, which branches$/$branches provide education.

$$N$$V relationship includes the number, name and rectorate address of each university included in the $$SYS system.

$$ Y$$PROG relationship shows the code, name, affiliated university, duration of education and city of each higher education program included in the $$SYS system.

$$ ADAY relationship, each candidate applying to $$SYS has the number, name, surname; the code, type and branch of the school they graduated from and the code of the higher education program they were accepted to$.$ For candidates who could not be accepted to any higher education program, the value of this last attribute is null.

$$ TERC$$H relationship, the data on which higher education programs each candidate preferred and in which order are included.

$1.$ Create the existence$-$relationship diagram of this database $($Show existence dependencies with weak existence sets in the diagram, use only binary relation sets and try to use as few relation sets as possible$).$

$2.$ Answer the following queries about the Database with the given relational schema using relational operators and SQL$.$

a$)$ "Find the number, name and surname of candidates who did not make any preferences".

b$)$ "Find the number, name and surname of candidates who were accepted to the higher education program they wanted as their $1$st preference".

c$)$ "Find the codes of higher education programs that were not preferred by any candidate as their $1$st preference".

d$)$ "Find the number, name and surname of candidates who included all higher education programs in Sakarya among their preferences".

e$)$ "Find the number, name and surname of candidates who did not include any higher education programs in Istanbul among their preferences".