College Algebra Problem Set No. 1

Name: ________________________      Course/Yr: _______________
Date: ________________________

Problem Set #1: SETS

A. Use the Roster Method to specify the sets of in Problems 1 through 5.
1. The fractions whose numerator is 1, and whose denominator is a counting number less than 10
2. The single digits used in the decimal system
3. The colors of the rainbow
4. The set of first 10 prime numbers
5. The months of the year

B. Write the cardinality of the sets in Problems 1 through 5.

C. The subsets of a set is given by the formula 2^n (read as "2 raised to n" or "2 raised to the power of n"), where n is the cardinality of the set. For example, the set {a, b, c} has 2^3 = 2x2x2 = 8 subsets, i.e., {{a,b,c},{a,b},{a,c},{b,c},{a},{b},{c},{Ø}}.
Find all the subsets of the set {l,o,v,e}.

D. If U = {x|x is a letter in the the English Alphabet}
   A = {x|x is a or one of the next four letters in the English alphabet}
     = {a,b,c,d,e}
   E = {x|x is e or one of the next four letters in the English alphabet}
   I = {x|x is i or one of the next four letters in the English alphabet},

Find:
  a. A n E
  b. E n I
  c. I n Ø
  d. Ø U A
  e. A' n I'

Answer to Analytic Geometry Knowledge Questions

Answers:

1.   c
2.   b
3.   b

Analytic Geometry Knowledge Questions

Direction: Encircle the letter of the correct answer.

1. A _________________ is an equation in r and Ө.
a. rectangular equation c.  polar equation
b. quadratic equation d.  parametric equation

2. It is a ray emanating from the pole of the rθ-plane.
a. Origin b. Polar Axis c. Polar Angle d. Angular Coordinate

3. It is a two-dimensional coordinate system in which each point P on a plane is determined by a distance r from a fixed point O and an angle Ө from a fixed direction.