Following is the schema of the product database:

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 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 (i.e., model is the primary key). The PCrelation givesfor eachmodel 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 Laptoprelation is similar, except that the screen size (in inches) is also included. The Printer relation records for each printer model whether the printerproduces color output (true if so), the process type (laser or inkjet, typically), and the price.

1. Find the printers with the highest price2. Find the laptops whose speed is slower than that of any PC.3. Find the model number of the item (PC, laptop, printer) with the highest price.4. Find the maker of the color printer with the lowest price.5. Find the maker(s) of the PC(s) with the fastest processor among all these PC's that have the smallest amount of RAM.6. Find the average price of PC's and laptops made by manufacturer "D".7. Find, for each different speed, the average price of a PC.8. Find those hard-disk sizes that occur in two or more PC's.9. Find those pairs of PC models that have both the same speed and RAM. A pair should be listed only once ; list (i,j) but not (j,i)10. Find those manufacturers of at least two different computers (PC's or Laptops) with speeds at least 3.0.

1. Write the relational algebra expression for each query.

All algebraic expression should be contained in a single plain text file with a .pdf extension. You can hand write them as well, as long as they are legible enough.