Exercise $2\mathrm{.}3\mathrm{.}1$: In this exercise we introduce one of our running examples of a relational database schema. The database schema consists of four relations, whose schemas are:

Product $($maker$,$ model, type$)$

PC$($model$,$ speed, ram, hd$,$ price$)$

Laptop$($model$,$ speed, ram, hd$,$ screen, price$)$

Printer$($model$,$ color, type, price$)$

The Product relation gives the manufacturer, model number and type $($PC$,$ laptop, or printer$)$ of various products. We assume for convenience that model numbers are unique over all manufacturers and product types; that assumption is not realistic, and a real database would include a code for the manufacturer as part of the model number. The PC relation gives for each model number that is a PC the speed $($of the processor, in gigahertz$),$ the amount of RAM $($in megabytes$),$ the size of the hard disk $($in gigabytes$),$ and the price. The Laptop relation is similar, except that the screen size $($in inches$)$ is also included. The Printer relation records for each printer model whether the printer produces color output $($true$,$ if so$),$ the process type $($laser or ink$-$jet, typically$),$ and the price.

Write the following declarations:

a$)$ A suitable schema for relation Product.

b$)$ A suitable schema for relation PC$.$

c$)$ A suitable schema for relation Laptop.

d$)$ A suitable schema for relation Printer.

e$)$ An alteration to your Printer schema from $($d$)$ to delete the attribute color.

f$)$ An alteration to your Laptop schema from $($c$)$ to add the attribute od $($optical$-$disk type, e$.$g$.,$ cd or dvd$).$ Let the default value for this attribute be 'none' if the laptop does not have an optical disk.