Relational Algebra $/$Calculus

Given the following database scheme:

CUSTOMER $($Cust#$,$ Cust$\_$Name, Cust$\_$City$)$

ORDER $($Order#$,$ Ord$\_$Date, Cust#$,$ Ord$\_$Amt$)$

ORDER$\_$ITEM $($Order#$,$ Item#$,$ Qty$)$

ITEM $($Item#$,$ Item$\_$Name, Unit$\_$Price$)$

SHIPMENT $($Order#$,$ Warehouse#$,$ Ship$\_$Date$)$

WAREHOUSE $($Warehouse#$,$ Warehouse$\_$City$)$

WAREHOUSE$\_$ITEM $($Item#$,$ Warehouse#$,$ Qty$)$

Write down relational expressions $($either relational algebra or relational calculus$)$ for the following queries.

$($a$)$ List the Order# and Ship$\_$Date for all orders shipped from Warehouse# $10.$

$($b$)$ List Order#$,$ Ord$\_$Date and Ship$\_$Date for orders which have not been shipped $($Hint: items are not shipped if

ship$\_$date is null$).$

$($c$)$ Produce a list of Item# that is not found in any warehouse in Melbourne.

$($d$)$ List Item#$,$ and Item$\_$Name that are stored in all warehouses in Sydney.

$($e$)$ List the Cname and City of the customers who have ordered the most $($in terms of money$).$