Convert the following SQL statements to relational algebra:

$1.$ select $*$ from students;

$2.$ select city from students;

$3.$ select major from students where gpa $>3\mathrm{.}0$;

$4.$ select name, age from students where gpa $<3\mathrm{.}0$ and dept $=$CS$$;

$5.$ select S$.$name, T$.$courseId

from students as S$,$ takes as T

where S$.$sid $=$ T$.$sid and S$.$dept $=$CS$$;

$6.$ select S$.$name, S$.$dept, T$.$cName

from student as S$,$ takes as T

where S$.$gpa $=3\mathrm{.}0$;

$7.($select name

from student

where dept $=$CS$)$

intersect

$($select name

from student

where gpa $>3\mathrm{.}0)$;

$8.($select name

from student

where dept $=$CS$)$

except

$($select name

from student

where gpa $>3\mathrm{.}0)$;

$9.$ select S$.$name, T$.$name

from student as S$,$ student as T

where S$.$gpa $=$ T$.$gpa;