Name: ___________________

Date:___________________

kwizNET Subscribers, please login to turn off the Ads!
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!

High School Mathematics
8.1 Cartesian Product of Sets

If A and B are any two sets, the set of all possible ordered pairs (a,b) with a A and b B, is called the cartesian product of A and B and is denoted by A B. and it is read as A cross B.
The set builder form of A B is
A B = {(a,b)/a A and b B}
Observing the above relation we find the following points.
1. The ordered pair of A B, the first coordinate belongs to A while the second coordinate belongs to B.
2. A B B A.
3. If n(A)= a and n(B) = b then n(A B) = ab.
4. If A is empty or B is empty then A B is empty.
5. If one of the sets A and B is infinite the other is non-empty then A B is also infinite.

Example:
If A = {1,3,5} and B = {2,4}, then find A B and B A and also find n(A B).
Solution:
(i). A B = {1,3,5} {2,4}
= {(1,2),(1,4),(3,2),(3,4),(5,2),(5,4)}

(ii). B A = {2,4} {1,3,5}
= {(2,1),(2,3),(2,5),(4,1),(4,3),(4,5)}

(iii). n(A B) = n(A) * n(B)
Where n(A) and n(B) are the number of elements in the set A and B respectively.
n(A B) = 3 * 2
= 6


Directions: Choose the correct answer. Also write at least 5 examples of your own.
Q 1: If A = {1,2,3} and B = {3,4} then find A B.
{(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)}
{(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)}
{(1,3),(1,5),(2,3),(2,4),(3,3),(3,4)}
{(1,3),(1,4),(3,2),(2,4),(3,3),(3,4)}

Q 2: If A = {2,3,4} and B = {5,6} then find A B.
{(2,5),(2,6),(3,5),(3,6),(4,2),(4,6)}
{(2,5),(2,6),(3,6),(3,6),(4,5),(4,6)}
{(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)}
{(2,5),(2,4),(3,5),(3,6),(4,5),(4,6)}

Q 3: If A = {2,4,6} and B = {1,3} then find B A.
{(1,2),(1,4),(1,6),(3,2),(3,1),(3,6)}
{(1,3),(1,4),(1,6),(3,2),(3,4),(3,6)}
{(1,2),(1,4),(1,6),(3,1),(3,4),(3,6)}
{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6)}

Q 4: If A = {1,2,3,4} and B = {6,7} then find A B.
{(1,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}
{(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}
{(1,6),(1,8),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}
{(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,5)}

Q 5: If A = {2,3,4} and B = {5,6} then find n(A B).
26
28
25
24

Q 6: If A = {1,2,3} and B = {4,5} then find B A.
{(1,4),(1,5),(2,3),(2,5),(3,4),(3,5)}
{(1,3),(1,5),(2,4),(2,3),(3,4),(3,5)}
{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)}
{(1,4),(1,2),(2,4),(2,5),(3,4),(3,5)}

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


Subscription to kwizNET Learning System costs less than $1 per month & offers the following benefits:

  • Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets
  • Instant scoring of online quizzes
  • Progress tracking and award certificates to keep your student motivated
  • Unlimited practice with auto-generated 'WIZ MATH' quizzes
  • Child-friendly website with no advertisements


© 2003-2007 kwizNET Learning System LLC. All rights reserved. This material may not be reproduced, displayed, modified or distributed without the express prior written permission of the copyright holder. For permission, contact info@kwizNET.com
For unlimited printable worksheets & more, go to http://www.kwizNET.com.