In addition, provide an explanation for each business rule in the following format:

"A relationship between customer and purchase $($see above$)$ is $1$:M as every customer may have many purchases and each purchase belongs to only one customer. The relationship is optional on the $$many$$ side because business rules say that every customer $$may$$ have a purchase. It is mandatory on the $$one$$ side because business rules say that every purchase $$must$$ belong to a customer. According to business rules, the cardinality on the many sides is $(0,$ N$)$ because it is optional and $(1,1)$ for the one side because it is mandatory. A weak relationship will be used as purchases are not dependent on customers. $"$

$.$