1. Given two relations R1 and R2, where R1 contains N1 tuples and R2 contains N2 tuples, and N2>N1> 0, give the maximum and minimum possible sizes (in tuples) for the result relation produced by each of the following relational algebra expressions. In each case, state any assumptions about the schemas for R1 and R2 that are needed to make the expression meaningful.
(a) R1 U R2
(b) R1 ∩ R2
(c) R1 - R2
(d) R1 x R2

Jason works as an accountant in a department store. he needs to keep a daily record of all the invoices issued by the store. which file naming convention would him the most?

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?

Jack is assisting his younger sibling mary with her mathematics assignment, which includes a study of the number system. jack explains to mary that whole numbers are counting numbers that could be used to record the number of fruits in a basket. which data type represents whole numbers? a. integers. b.floating-point numbers. c. strings. d.boolean