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

When the pc version of the spreadsheet program became available, the ibm pc quickly became the top-selling personal computer?

Robots with telescoping arms are sometimes used to perform tasks (e.g., welding or placing screws) where access may be difficult for other robotic types. during a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. use a computer program to plot the path of tip a in x and y coordinates for 0 ≤ t ≤ 4s.

What is the first view you place in your drawing?