Consider we have a database with $7$ relations whose schema is shown as below:

Customer $=\{$cid$,$ f name, lname$,$ birthday, income$\}$

Account $=\{$accno$,$type, balance, branch no$\}$

Owns $=\{$cid$,$ accno$\}$

Transactions $=\{$txn no$,$ accno, amount, date, note,txn type$\}$

Employee $=\{$eid$,$ f name, lname$,$ salary, start date, branch no$\}$

PersonalBanker $=\{$cid$,$ eid, assignment date$\}$

Branch $=\{$branch no$,$ branch name, street, num employee, manager eid, budget$\}$

Write a relational algebra query AND a tuple relational calculus $($TRC$)$ query to answer each of the

following questions. You may use input relation names to differentiate between attributes with the same

name in the results of a join or Cartesian product $($such as referring to Employee. f name or Customer. f name

in the results of the Cartesian product of Employee and Customer$).$ Note that you can use comparison

operators $($e$.$g$.<,>,<=,$ etc.$)$ over dates.

Note: You should ONLY use relational algebra and calculus notations that we covered in the class.

$(1)$ Find the first name, last name, the branch name, and number of employees for all managers who serve

as both a personal banker and a manager.

$(2)$ Find the first and last names of customers who were born after June $2$nd$,2001$ and whose income is

greater than $$100,000.$

$(3)$ Find the CIDs, first names, last names and birthday of customers who have an account at a branch

with more than $25$ employees.

$(4)$ Find the CIDs of customers who do not own a joint account $($an account that is owned by more than

one customer$).$

$5)$ Find the CIDs of customers who have personal bankers in both $$Pittsburgh West$$ and $$Harrisburg

South$$ branches.

$(6)$ Find the branch names of branches that employ at least one employee whose last name is $$Jackson$,$

and also at least one employee making less than $$20,000.$

$(7)$ Find the CIDs of customers whose accounts have a transaction of type check where the absolute value

of the transactions amount is greater than $$10,000($i$.$e$.$ they deposited a check greater than $$10,000$

or paid using a check an amount greater than $$10,000).$

$(8)$ Find the first names, last names and birth dates of the customers whose have the lowest income among

all the customers who were born before August $211950.($If more than one customer have the lowest

income among this group, return all of them.$)$

$(9)$ Find EIDs and salaries of employees who earn more than the manager of their branch.

$(10)$ Find the first names, last names, and income of customers who own at least an account in all branches.

$(11)[5$ pts$]$ Find all customers who have an account at every branch with a budget between $$20,000$ and

$$200,000.$