Following is the relational schema and I want to write queries using Relational algebra to answer the following question:

Please make sure the queries are in Relational algebra. I cannot stress this enough DO NOT USE SQL, USE RELATIONAL ALGEBRA.

Relational schema of question

1. Product(model, maker, type)

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

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

Printer(model, color, type, price)

1. List the models and prices of all Laptop's with the most expensive first.

2. List the model and price of the Laptops with more than 512 KB RAM and faster than 1.60.

3. List all manufacturers who make PCs.

4. List the model and manufacturer of all Laptops costing less than $ 1,000.

5. List the names and models of the manufacturers who make PCs and laptops with speeds greater than 2. 6) Which manufacturers make PCs, but not printers?