1. For each integer i define Ai as follows:
If i is even then Ai = {x | x is integer and x<-i or i<x }
If i is odd the Ai = {x | x is integer and -i<x<i }
a) Describe each of the sets A0, A1, A2, A-1 and A-2 (25 points)
b) Find the union of the collection { Ai | i belongs to {1, 3, 5, 7}} (20 points)
2. For each of the following strings, find an appropriate alphabet of elements for the string. (25 points)
a) x+3
b) x+y=3y+4
c) 12310
d) 297.34001
e) This is a sentence ending with a period..
3. Represent each relation as a set:
a) R = { <x,y,z> | x=y+z where x, y, z, belong to {1, 2, 3}} (5 points)
b) <x,y> belongs to U if and only if x belongs to {a,b} and y belongs to {1,2}. (5 points)
4. 15 (page 315) (5 points)
Maximum mark: 85 (100%)