Problem $3.(50$ points$)$ Consider the following relational database:

customer$($customer$\_$ID$,$ name, address$)$

product $($product$\_$ID$,$ price$)$

purchase$($purchase$\_$ID$,$ customer$\_$ID$,$ product$\_$ID$,$ quantity, date$)$

Assume that $($i$)$ each customer is assigned a unique ID$,($ii$)$ each product is assigned a unique

ID$,$ and $($iii$)$ each purchase is assigned a unique ID$.$

$($a$)(10$ points$)$ Provide an example $($a relation instance$)$ which shows that $\{$customer$\_$ID$,$ name$\}$

is a superkey but name