Question $2.[12$ MARKS$]$

Below is a slightly simplified version of a schema we used in lecture. A course's cName attribute gives its

full name, such as "Introduction to Databases", while dept has a value such as $"$CSC$"$ and cNum has a

value such as $343.$

Student$($sID$,$ surName, firstName$)$

Offering$[$dept$,$ cNum$]$ sube Course$[$dept$,$ cNum$]$

Course$($dept$,$ cNum, cName$)$

Offering$(),$ dept, cNum, term, instructor$)$

Took sID$]$ sube Student sID$]$

Took $[oID]sube$ Offering oID

Took$($sID$,$ oID, grade$)$

Write a query in relational algebra that finds the SID and surname of each student who has a passing grade

in every first$-$year course ever offered by department 'BIO', but never took a course offered by department

'CHE'. A first$-$year course is one whose cNum is between $100$ and $199$ inclusive. A passing grade is a grade

over $50.$ Use only the basic operators :$=.$ Continue your answer on the next page if

needed.

Hint: As a first step, write the left$-$hand sides of a series of assignment statements; use good names

for the intermediate relations. This will help you solve the question, and also to earn part marks if you

make a mistake.