**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%)